-
question_answer1)
The perimeter of a triangle with sides \[3\mathbf{i}+4\mathbf{j}+5\mathbf{k},\,\] \[4\mathbf{i}-3\mathbf{j}-5\mathbf{k}\] and \[7\mathbf{i}+\mathbf{j}\] is [MP PET 1991]
A)
\[\sqrt{450}\] done
clear
B)
\[\sqrt{150}\] done
clear
C)
\[\sqrt{50}\] done
clear
D)
\[\sqrt{200}\] done
clear
View Solution play_arrow
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question_answer2)
If the position vectors of the vertices of a triangle be \[2\mathbf{i}+4\mathbf{j}-\mathbf{k},\] \[4\mathbf{i}+5\mathbf{j}+\mathbf{k}\] and \[3\mathbf{i}+6\mathbf{j}-3\mathbf{k},\] then the triangle is [UPSEAT 2004]
A)
Right angled done
clear
B)
Isosceles done
clear
C)
Equilateral done
clear
D)
Right angled isosceles done
clear
View Solution play_arrow
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question_answer3)
If one side of a square be represented by the vector \[3\mathbf{i}+4\mathbf{j}+5\mathbf{k},\] then the area of the square is
A)
12 done
clear
B)
13 done
clear
C)
25 done
clear
D)
50 done
clear
View Solution play_arrow
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question_answer4)
If \[\mathbf{a}=2\mathbf{i}+2\mathbf{j}-\mathbf{k}\] and \[|x\,\mathbf{a}|\,\,=1,\] then x =
A)
\[\pm \frac{1}{3}\] done
clear
B)
\[\pm \frac{1}{4}\] done
clear
C)
\[\pm \frac{1}{5}\] done
clear
D)
\[\pm \frac{1}{6}\] done
clear
View Solution play_arrow
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question_answer5)
Which of the following is not a unit vector for all values of q
A)
\[(\cos \theta )\mathbf{i}-(\sin \theta )\,\mathbf{j}\] done
clear
B)
\[(\sin \theta )\,\mathbf{i}+(\cos \theta )\,\mathbf{j}\] done
clear
C)
\[(\sin \,\,2\theta )\,\mathbf{i}-(\cos \theta )\,\mathbf{j}\] done
clear
D)
\[(\cos \,\,2\theta )\,\mathbf{i}-(\sin \,\,2\theta )\,\mathbf{j}\] done
clear
View Solution play_arrow
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question_answer6)
If \[\mathbf{a}+\mathbf{b}\] bisects the angle between a and b, then a and b are
A)
Mutually perpendicular done
clear
B)
Unlike vectors done
clear
C)
Equal in magnitude done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer7)
If \[\mathbf{a}=\mathbf{i}+2\mathbf{j}+2\mathbf{k}\] and \[\mathbf{b}=3\mathbf{i}+6\mathbf{j}+2\mathbf{k},\] then a vector in the direction of a and having magnitude as |b| is [IIT 1983]
A)
\[7\,(\mathbf{i}+\mathbf{j}+\mathbf{k})\] done
clear
B)
\[\frac{7}{3}\,(\mathbf{i}+2\mathbf{j}+2\mathbf{k})\] done
clear
C)
\[\frac{7}{9}\,(\mathbf{i}+2\mathbf{j}+2\,\mathbf{k})\] done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer8)
If \[\mathbf{p}=7\mathbf{i}-2\mathbf{j}+3\mathbf{k}\] and \[\mathbf{q}=3\mathbf{i}+\mathbf{j}+5\mathbf{k},\] then the magnitude of \[\mathbf{p}-2\mathbf{q}\] is [MP PET 1987]
A)
\[\sqrt{29}\] done
clear
B)
4 done
clear
C)
\[\sqrt{62}-2\sqrt{35}\] done
clear
D)
\[\sqrt{66}\] done
clear
View Solution play_arrow
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question_answer9)
Let \[\mathbf{a}=\mathbf{i}\] be a vector which makes an angle of \[{{120}^{o}}\] with a unit vector b. Then the unit vector \[(\mathbf{a}+\mathbf{b})\] is [MP PET 1991]
A)
\[-\frac{1}{2}\mathbf{i}+\frac{\sqrt{3}}{2}\mathbf{j}\] done
clear
B)
\[-\frac{\sqrt{3}}{2}\mathbf{i}+\frac{1}{2}\mathbf{j}\] done
clear
C)
\[\frac{1}{2}\mathbf{i}+\frac{\sqrt{3}}{2}\mathbf{j}\] done
clear
D)
\[\frac{\sqrt{3}}{2}\mathbf{i}-\frac{1}{2}\mathbf{j}\] done
clear
View Solution play_arrow
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question_answer10)
If the position vectors of the vertices of a triangle be \[6\mathbf{i}+4\mathbf{j}+5\mathbf{k},\,\,\,4\mathbf{i}+5\mathbf{j}+6\mathbf{k}\] and \[5\mathbf{i}+6\mathbf{j}+4\mathbf{k},\] then the triangle is
A)
Right angled done
clear
B)
Isosceles done
clear
C)
Equilateral done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer11)
The perimeter of the triangle whose vertices have the position vectors \[(\mathbf{i}+\mathbf{j}+\mathbf{k}),\,\,(5\mathbf{i}+3\mathbf{j}-3\mathbf{k})\] and \[(2\mathbf{i}+5\mathbf{j}+9\mathbf{k}),\] is given by [MP PET 1993]
A)
\[15+\sqrt{157}\] done
clear
B)
\[15-\sqrt{157}\] done
clear
C)
\[\sqrt{15}-\sqrt{157}\] done
clear
D)
\[\sqrt{15}+\sqrt{157}\] done
clear
View Solution play_arrow
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question_answer12)
The position vectors of two points A and B are \[\mathbf{i}+\mathbf{j}-\mathbf{k}\] and \[2\mathbf{i}-\mathbf{j}+\mathbf{k}\] respectively. Then \[|\overrightarrow{AB}|\,\,=\] [BIT Ranchi 1992]
A)
2 done
clear
B)
3 done
clear
C)
4 done
clear
D)
5 done
clear
View Solution play_arrow
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question_answer13)
The magnitudes of mutually perpendicular forces a, b and c are 2, 10 and 11 respectively. Then the magnitude of its resultant is [IIT 1984]
A)
12 done
clear
B)
15 done
clear
C)
9 done
clear
D)
None done
clear
View Solution play_arrow
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question_answer14)
The system of vectors \[\mathbf{i},\,\,\mathbf{j},\,\,\mathbf{k}\] is
A)
Orthogonal done
clear
B)
Coplanar done
clear
C)
Collinear done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer15)
The direction cosines of the resultant of the vectors \[(\mathbf{i}+\mathbf{j}+\mathbf{k}),\] \[(-\mathbf{i}+\mathbf{j}+\mathbf{k}),\] \[(\mathbf{i}-\mathbf{j}+\mathbf{k})\] and \[(\mathbf{i}+\mathbf{j}-\mathbf{k}),\] are
A)
\[\left( \frac{1}{\sqrt{2}},\,\,\frac{1}{\sqrt{3}},\,\,\frac{1}{\sqrt{6}} \right)\] done
clear
B)
\[\left( \frac{1}{\sqrt{6}},\,\,\frac{1}{\sqrt{6}},\,\,\frac{1}{\sqrt{6}} \right)\] done
clear
C)
\[\left( -\frac{1}{\sqrt{6}},\,\,-\frac{1}{\sqrt{6}},\,-\,\frac{1}{\sqrt{6}} \right)\] done
clear
D)
\[\left( \frac{1}{\sqrt{3}},\,\,\frac{1}{\sqrt{3}},\,\frac{1}{\sqrt{3}} \right)\] done
clear
View Solution play_arrow
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question_answer16)
The position vectors of P and Q are \[5\mathbf{i}+4\mathbf{j}+a\mathbf{k}\] and \[-\mathbf{i}+2\mathbf{j}-2\mathbf{k}\] respectively. If the distance between them is 7, then the value of a will be
A)
5, 1 done
clear
B)
5, 1 done
clear
C)
0, 5 done
clear
D)
1, 0 done
clear
View Solution play_arrow
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question_answer17)
A zero vector has
A)
Any direction done
clear
B)
No direction done
clear
C)
Many directions done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer18)
A unit vector a makes an angle \[\frac{\pi }{4}\] with z-axis. If \[\mathbf{a}+\mathbf{i}+\mathbf{j}\] is a unit vector, then a is equal to [IIT 1988]
A)
\[\frac{\mathbf{i}}{2}+\frac{\mathbf{j}}{2}+\frac{\mathbf{k}}{\sqrt{2}}\] done
clear
B)
\[\frac{\mathbf{i}}{2}+\frac{\mathbf{j}}{2}-\frac{\mathbf{k}}{\sqrt{2}}\] done
clear
C)
\[-\frac{\mathbf{i}}{2}-\frac{\mathbf{j}}{2}+\frac{\mathbf{k}}{\sqrt{2}}\] done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer19)
A force is a
A)
Unit vector done
clear
B)
Localised vector done
clear
C)
Zero vector done
clear
D)
Free vector done
clear
View Solution play_arrow
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question_answer20)
If a, b, c, d be the position vectors of the points A, B, C and D respectively referred to same origin O such that no three of these points are collinear and \[\mathbf{a}+\mathbf{c}=\mathbf{b}+\mathbf{d},\] then quadrilateral ABCD is a
A)
Square done
clear
B)
Rhombus done
clear
C)
Rectangle done
clear
D)
Parallelogram done
clear
View Solution play_arrow
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question_answer21)
If the position vectors of A and B are \[\mathbf{i}+3\mathbf{j}-7\mathbf{k}\] and \[5\mathbf{i}-2\mathbf{j}+4\mathbf{k},\] then the direction cosine of \[\overrightarrow{AB}\] along y-axis is [MNR 1989]
A)
\[\frac{4}{\sqrt{162}}\] done
clear
B)
\[-\frac{5}{\sqrt{162}}\] done
clear
C)
5 done
clear
D)
11 done
clear
View Solution play_arrow
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question_answer22)
If the resultant of two forces is of magnitude P and equal to one of them and perpendicular to it, then the other force is [MNR 1986]
A)
\[P\sqrt{2}\] done
clear
B)
P done
clear
C)
\[P\sqrt{3}\] done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer23)
The direction cosines of vector \[\mathbf{a}=3\mathbf{i}+4\mathbf{j}+5\mathbf{k}\] in the direction of positive axis of x, is [MP PET 1991]
A)
\[\pm \frac{3}{\sqrt{50}}\] done
clear
B)
\[\frac{4}{\sqrt{50}}\] done
clear
C)
\[\frac{3}{\sqrt{50}}\] done
clear
D)
\[-\frac{4}{\sqrt{50}}\] done
clear
View Solution play_arrow
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question_answer24)
The point having position vectors \[2\mathbf{i}+3\mathbf{j}+4\mathbf{k},\,\,\]\[3\mathbf{i}+4\mathbf{j}+2\mathbf{k},\] \[4\mathbf{i}+2\mathbf{j}+3\mathbf{k}\] are the vertices of [EAMCET 1988]
A)
Right angled triangle done
clear
B)
Isosceles triangle done
clear
C)
Equilateral triangle done
clear
D)
Collinear done
clear
View Solution play_arrow
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question_answer25)
Let \[\alpha ,\,\,\beta ,\,\,\gamma \] be distinct real numbers. The points with position vectors \[\alpha \mathbf{i}+\beta \mathbf{j}+\gamma \mathbf{k},\,\,\beta \mathbf{i}+\gamma \mathbf{j}+\alpha \mathbf{k},\,\,\gamma \mathbf{i}+\alpha \mathbf{j}+\beta \mathbf{k}\] [IIT Screening 1994]
A)
Are collinear done
clear
B)
Form an equilateral triangle done
clear
C)
Form a scalene triangle done
clear
D)
Form a right angled triangle done
clear
View Solution play_arrow
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question_answer26)
If \[|\mathbf{a}|\,\,=3,\,\,\,|\mathbf{b}|\,\,=4\] and \[|\mathbf{a}+\mathbf{b}|\,\,=5,\] then \[|\mathbf{a}-\mathbf{b}|\,\,=\] [EAMCET 1994]
A)
6 done
clear
B)
5 done
clear
C)
4 done
clear
D)
3 done
clear
View Solution play_arrow
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question_answer27)
If OP = 8 and \[\overrightarrow{OP}\] makes angles \[{{45}^{o}}\] and \[{{60}^{o}}\] with OX-axis and OY-axis respectively, then \[\overrightarrow{OP}=\]
A)
\[8\,(\sqrt{2}\mathbf{i}+\mathbf{j}\pm \mathbf{k})\] done
clear
B)
\[4\,(\sqrt{2}\mathbf{i}+\mathbf{j}\pm \mathbf{k})\] done
clear
C)
\[\frac{1}{4}(\sqrt{2}\mathbf{i}+\mathbf{j}\pm \mathbf{k})\] done
clear
D)
\[\frac{1}{8}(\sqrt{2}\mathbf{i}+\mathbf{j}\pm \mathbf{k})\] done
clear
View Solution play_arrow
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question_answer28)
If a and b are two non-zero and non-collinear vectors, then a + b and a ? b are [MP PET 1997]
A)
Linearly dependent vectors done
clear
B)
Linearly independent vectors done
clear
C)
Linearly dependent and independent vectors done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer29)
If the vectors \[6\mathbf{i}-2\mathbf{j}+3\mathbf{k},\,\,2\mathbf{i}+3\mathbf{j}-6\mathbf{k}\] and \[3\mathbf{i}+6\mathbf{j}-2\mathbf{k}\] form a triangle, then it is [Karnataka CET 1999]
A)
Right angled done
clear
B)
Obtuse angled done
clear
C)
Equilteral done
clear
D)
Isosceles done
clear
View Solution play_arrow
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question_answer30)
If the resultant of two forces of magnitudes P and Q acting at a point at an angle of \[{{60}^{o}}\] is \[\sqrt{7}Q,\] then P/Q is [Roorkee 1999]
A)
1 done
clear
B)
\[\frac{3}{2}\] done
clear
C)
2 done
clear
D)
4 done
clear
View Solution play_arrow
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question_answer31)
The direction cosines of the vector \[3\mathbf{i}-4\mathbf{j}+5\mathbf{k}\] are [Karnataka CET 2000]
A)
\[\frac{3}{5},\,\frac{-4}{5},\frac{1}{5}\] done
clear
B)
\[\frac{3}{5\sqrt{2}},\,\frac{-4}{5\sqrt{2}},\frac{1}{\sqrt{2}}\] done
clear
C)
\[\frac{3}{\sqrt{2}},\,\frac{-4}{\sqrt{2}},\,\frac{1}{\sqrt{2}}\] done
clear
D)
\[\frac{3}{5\sqrt{2}},\,\,\frac{4}{5\sqrt{2}},\,\frac{1}{\sqrt{2}}\] done
clear
View Solution play_arrow
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question_answer32)
The position vectors of A and B are \[2\mathbf{i}-9\mathbf{j}-4\mathbf{k}\] and \[6\mathbf{i}-3\mathbf{j}+8\mathbf{k}\] respectively, then the magnitude of \[\overrightarrow{AB}\] is [MP PET 2000]
A)
11 done
clear
B)
12 done
clear
C)
13 done
clear
D)
14 done
clear
View Solution play_arrow
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question_answer33)
If the position vectors of P and Q are \[(\mathbf{i}+3\mathbf{j}-7\mathbf{k})\] and \[(5\mathbf{i}-2\mathbf{j}+4\mathbf{k}),\] then \[|\overrightarrow{PQ}|\] is [MP PET 2001, 03]
A)
\[\sqrt{158}\] done
clear
B)
\[\sqrt{160}\] done
clear
C)
\[\sqrt{161}\] done
clear
D)
\[\sqrt{162}\] done
clear
View Solution play_arrow
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question_answer34)
If a is non zero vector of modulus a and m is a non-zero scalar, then ma is a unit vector if [MP PET 2002]
A)
\[m=\pm 1\] done
clear
B)
\[m=\,\,|\mathbf{a}|\] done
clear
C)
\[m=\frac{1}{|\mathbf{a}|}\] done
clear
D)
\[m=\pm \,2\] done
clear
View Solution play_arrow
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question_answer35)
The position vectors of the points A, B, C are \[(2\mathbf{i}+\mathbf{j}-\mathbf{k}),\] \[(3\mathbf{i}-2\mathbf{j}+\mathbf{k})\] and \[(\mathbf{i}+4\mathbf{j}-3\mathbf{k})\] respectively. These points [Kurukshetra CEE 2002]
A)
Form an isosceles triangle done
clear
B)
Form a right-angled triangle done
clear
C)
Are collinear done
clear
D)
Form a scalene triangle done
clear
View Solution play_arrow
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question_answer36)
The vectors \[\overrightarrow{AB}=3\mathbf{i}+4\mathbf{k},\] and \[\overrightarrow{AC}=5\mathbf{i}-2\mathbf{j}+4\mathbf{k}\] are the sides of a triangle ABC. The length of the median through A is [AIEEE 2003]
A)
\[\sqrt{18}\] done
clear
B)
\[\sqrt{72}\] done
clear
C)
\[\sqrt{33}\] done
clear
D)
\[\sqrt{288}\] done
clear
View Solution play_arrow
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question_answer37)
If the position vectors of the vertices A, B, C of a triangle ABC are \[7\mathbf{j}+10\mathbf{k},\] \[-\mathbf{i}+6\mathbf{j}+6\mathbf{k}\] and \[-4\mathbf{i}+9\mathbf{j}+6\mathbf{k}\] respectively, the triangle is [UPSEAT 2004]
A)
Equilateral done
clear
B)
Isosceles done
clear
C)
Scalene done
clear
D)
Right angled and isosceles also done
clear
View Solution play_arrow
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question_answer38)
The figure formed by the four points \[\mathbf{i}+\mathbf{j}-\mathbf{k},\,\,\,2\mathbf{i}+3\mathbf{j},\] \[3\mathbf{i}+5\mathbf{j}-2\mathbf{k}\] and \[\mathbf{k}-\mathbf{j}\] is [MP PET 2004]
A)
Rectangle done
clear
B)
Parallelogram done
clear
C)
Trapezium done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer39)
ABC is an isosceles triangle right angled at A. Forces of magnitude \[2\sqrt{2,}\,5\] and 6 act along \[\overrightarrow{BC},\,\,\overrightarrow{CA}\] and \[\overrightarrow{AB}\] respectively. The magnitude of their resultant force is [Roorkee 1999]
A)
4 done
clear
B)
5 done
clear
C)
\[11+2\sqrt{2}\] done
clear
D)
30 done
clear
View Solution play_arrow
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question_answer40)
If ABCDEF is a regular hexagon and \[\overrightarrow{AB}+\overrightarrow{AC}+\overrightarrow{AD}+\overrightarrow{AE}+\overrightarrow{AF}=\lambda \,\overrightarrow{AD},\] then \[\lambda =\] [RPET 1985]
A)
2 done
clear
B)
3 done
clear
C)
4 done
clear
D)
6 done
clear
View Solution play_arrow
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question_answer41)
If P and Q be the middle points of the sides BC and CD of the parallelogram ABCD, then \[\overrightarrow{AP}+\overrightarrow{AQ}=\]
A)
\[\overrightarrow{AC}\] done
clear
B)
\[\frac{1}{2}\overrightarrow{AC}\] done
clear
C)
\[\frac{2}{3}\overrightarrow{AC}\] done
clear
D)
\[\frac{3}{2}\overrightarrow{AC}\] done
clear
View Solution play_arrow
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question_answer42)
P is a point on the side BC of the \[\Delta \,ABC\] and Q is a point such that \[\overrightarrow{PQ}\] is the resultant of \[\overrightarrow{AP},\,\overrightarrow{PB},\,\overrightarrow{PC}.\] Then ABQC is a
A)
Square done
clear
B)
Rectangle done
clear
C)
Parallelogram done
clear
D)
Trapezium done
clear
View Solution play_arrow
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question_answer43)
In the figure, a vector x satisfies the equation \[\mathbf{x}-\mathbf{w}=\mathbf{v}\]. Then x =
A)
\[2\mathbf{a}+\mathbf{b}+\mathbf{c}\] done
clear
B)
\[\mathbf{a}+2\mathbf{b}+\mathbf{c}\] done
clear
C)
\[\mathbf{a}+\mathbf{b}+2\mathbf{c}\] done
clear
D)
\[\mathbf{a}+\mathbf{b}+\mathbf{c}\] done
clear
View Solution play_arrow
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question_answer44)
A vector coplanar with the non-collinear vectors a and b is
A)
\[\mathbf{a}\times \mathbf{b}\] done
clear
B)
\[l\ne 0,\,\,m\ne 0,\,\,n\ne 0\] done
clear
C)
\[\mathbf{a}\,.\,\mathbf{b}\] done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer45)
If ABCD is a parallelogram, \[\overrightarrow{AB}=2\,\mathbf{i}+4\,\mathbf{j}-5\,\mathbf{k}\] and \[\overrightarrow{AD}=\,\mathbf{i}+2\,\mathbf{j}+3\,\mathbf{k},\] then the unit vector in the direction of BD is [Roorkee 1976]
A)
\[\frac{1}{\sqrt{69}}\,(\mathbf{i}+2\mathbf{j}-8\mathbf{k})\] done
clear
B)
\[\frac{1}{69}\,(\mathbf{i}+2\mathbf{j}-8\,\mathbf{k})\] done
clear
C)
\[\frac{1}{\sqrt{69}}\,(-\mathbf{i}-2\mathbf{j}+8\mathbf{k})\] done
clear
D)
\[\frac{1}{69}\,(-\mathbf{i}-2\mathbf{j}+8\,\mathbf{k})\] done
clear
View Solution play_arrow
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question_answer46)
If a, b and c be three non-zero vectors, no two of which are collinear. If the vector \[\mathbf{a}+2\mathbf{b}\] is collinear with c and \[\mathbf{b}+3\mathbf{c}\] is collinear with a, then (\[\lambda \] being some non-zero scalar) \[\mathbf{a}+2\mathbf{b}+6\mathbf{c}\] is equal to [AIEEE 2004]
A)
\[\lambda \mathbf{a}\] done
clear
B)
\[\lambda \mathbf{b}\] done
clear
C)
\[\lambda \mathbf{c}\] done
clear
D)
0 done
clear
View Solution play_arrow
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question_answer47)
If \[\mathbf{a}=2\mathbf{i}+5\mathbf{j}\] and \[\mathbf{b}=2\mathbf{i}-\mathbf{j},\] then the unit vector along \[y=0\] will be [RPET 1985, 95]
A)
\[\frac{\mathbf{i}-\mathbf{j}}{\sqrt{2}}\] done
clear
B)
\[ap+bq+cr=0\] done
clear
C)
\[{{90}^{o}}\] done
clear
D)
\[\frac{\mathbf{i}+\mathbf{j}}{\sqrt{2}}\] done
clear
View Solution play_arrow
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question_answer48)
What should be added in vector \[\mathbf{a}=3\mathbf{i}+4\mathbf{j}-2\mathbf{k}\] to get its resultant a unit vector i [Roorkee 1977]
A)
\[-\,2\mathbf{i}-4\mathbf{j}+2\mathbf{k}\] done
clear
B)
\[-2\mathbf{i}+4\mathbf{j}-2\mathbf{k}\] done
clear
C)
\[2\mathbf{i}+4\mathbf{j}-2\mathbf{k}\] done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer49)
If \[\mathbf{a}=\mathbf{i}+2\mathbf{j}+3\mathbf{k},\,\,\,\mathbf{b}=-\mathbf{i}+2\mathbf{j}+\mathbf{k}\] and \[\mathbf{c}=3\mathbf{i}+\mathbf{j},\] then the unit vector along its resultant is [Roorkee 1980]
A)
\[3\mathbf{i}+5\mathbf{j}+4\mathbf{k}\] done
clear
B)
\[\frac{3\mathbf{i}+5\mathbf{j}+4\mathbf{k}}{50}\] done
clear
C)
\[\frac{3\mathbf{i}+5\mathbf{j}+4\mathbf{k}}{5\sqrt{2}}\] done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer50)
In a regular hexagon ABCDEF, \[\overrightarrow{AE}=\] [MNR 1984]
A)
\[2\mathbf{a}-3\mathbf{b}\] done
clear
B)
\[\overrightarrow{AC}\,\,+\,\,\overrightarrow{AF}\,\,-\,\overrightarrow{AB}\] done
clear
C)
\[\overrightarrow{AC}\,\,+\,\,\overrightarrow{AB}\,\,-\,\,\overrightarrow{AF}\] done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer51)
\[3\,\,\overrightarrow{OD}+\overrightarrow{DA}+\overrightarrow{DB}+\overrightarrow{DC}=\] [IIT 1988]
A)
\[\overrightarrow{OA}+\overrightarrow{OB}-\overrightarrow{OC}\] done
clear
B)
\[\overrightarrow{OA}+\overrightarrow{OB}-\overrightarrow{BD}\] done
clear
C)
\[\overrightarrow{OA}+\overrightarrow{OB}+\overrightarrow{OC}\] done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer52)
\[\mathbf{p}=2\mathbf{a}-3\mathbf{b},\,\,\,\mathbf{q}=\mathbf{a}-2\mathbf{b}+\mathbf{c},\,\,\mathbf{r}=-3\mathbf{a}+\mathbf{b}+2\mathbf{c};\] where a, b and c being non-zero, non-coplanar vectors, then the vector \[-2\mathbf{a}+3\mathbf{b}-\mathbf{c}\] is equal to
A)
\[\mathbf{p}-4\mathbf{q}\] done
clear
B)
\[\frac{-7\mathbf{q}+\mathbf{r}}{5}\] done
clear
C)
\[2\mathbf{p}-3\mathbf{q}+\mathbf{r}\] done
clear
D)
\[4\mathbf{p}-2\mathbf{r}\] done
clear
View Solution play_arrow
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question_answer53)
In a trapezium, the vector \[\overrightarrow{BC}=\lambda \overrightarrow{AD}.\] We will then find that \[\mathbf{p}=\overrightarrow{AC}+\overrightarrow{BD}\] is collinear with \[\overrightarrow{AD},\] If \[\mathbf{p}=\mu \overrightarrow{AD},\] then
A)
\[\mu =\lambda +1\] done
clear
B)
\[\lambda =\mu +1\] done
clear
C)
\[\lambda +\mu =1\] done
clear
D)
\[\mu =2+\lambda \] done
clear
View Solution play_arrow
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question_answer54)
If \[\mathbf{a}=2\mathbf{i}+\mathbf{j}-8\mathbf{k}\] and \[\mathbf{b}=\mathbf{i}+3\mathbf{j}-4\mathbf{k},\] then the magnitude of \[\mathbf{a}+\mathbf{b}=\] [MP PET 1996]
A)
13 done
clear
B)
\[\frac{13}{3}\] done
clear
C)
\[\frac{3}{13}\] done
clear
D)
\[\frac{4}{13}\] done
clear
View Solution play_arrow
-
question_answer55)
A, B, C, D, E are five coplanar points, then \[\overrightarrow{DA}+\overrightarrow{DB}+\overrightarrow{DC}+\overrightarrow{AE}+\overrightarrow{BE}+\overrightarrow{CE}\] is equal to [RPET 1999]
A)
\[\overrightarrow{DE}\] done
clear
B)
\[3\,\overrightarrow{DE}\] done
clear
C)
\[2\,\overrightarrow{DE}\] done
clear
D)
\[4\,\overrightarrow{ED}\] done
clear
View Solution play_arrow
-
question_answer56)
If \[\mathbf{a}=3\mathbf{i}-2\mathbf{j}+\mathbf{k},\,\,\mathbf{b}=2\mathbf{i}-4\mathbf{j}-3\mathbf{k}\] and \[\mathbf{c}=-\mathbf{i}+2\mathbf{j}+2\mathbf{k},\] then \[\mathbf{a}+\mathbf{b}+\mathbf{c}\] is [MP PET 2001]
A)
\[3\mathbf{i}-4\mathbf{j}\] done
clear
B)
\[3\mathbf{i}+4\mathbf{j}\] done
clear
C)
\[4\mathbf{i}-4\mathbf{j}\] done
clear
D)
\[4\mathbf{i}+4\mathbf{j}\] done
clear
View Solution play_arrow
-
question_answer57)
Five points given by A, B, C, D, E are in a plane. Three forces \[\overrightarrow{AC},\,\,\overrightarrow{AD}\] and \[\overrightarrow{AE}\] act at A and three forces \[\overrightarrow{CB},\,\,\overrightarrow{DB},\,\,\overrightarrow{EB}\] act at B. Then their resultant is [AMU 2001]
A)
\[2\overrightarrow{AC}\] done
clear
B)
\[3\overrightarrow{AB}\] done
clear
C)
\[3\overrightarrow{DB}\] done
clear
D)
\[2\overrightarrow{BC}\] done
clear
View Solution play_arrow
-
question_answer58)
The sum of two forces is 18 N and resultant whose direction is at right angles to the smaller force is 12N. The magnitude of the two forces are [AIEEE 2002]
A)
13, 5 done
clear
B)
12, 6 done
clear
C)
14, 4 done
clear
D)
11, 7 done
clear
View Solution play_arrow
-
question_answer59)
The unit vector parallel to the resultant vector of \[2\mathbf{i}+4\mathbf{j}-5\mathbf{k}\] and \[\mathbf{i}+2\mathbf{j}+3\mathbf{k}\] is [MP PET 2003]
A)
\[\frac{1}{7}\,(3\mathbf{i}+6\mathbf{j}-2\mathbf{k})\] done
clear
B)
\[\frac{\mathbf{i}+\mathbf{j}+\mathbf{k}}{\sqrt{3}}\] done
clear
C)
\[\frac{\mathbf{i}+\mathbf{j}+2\mathbf{k}}{\sqrt{6}}\] done
clear
D)
\[\frac{1}{\sqrt{69}}\,(-\mathbf{i}-\mathbf{j}+8\mathbf{k})\] done
clear
View Solution play_arrow
-
question_answer60)
If a, b, c are the position vectors of the vertices A, B, C of the triangle ABC, then the centroid of \[\Delta \,ABC\] is [MP PET 1987]
A)
\[\frac{\mathbf{a}+\mathbf{b}+\mathbf{c}}{3}\] done
clear
B)
\[\frac{1}{2}\,\left( \mathbf{a}+\frac{\mathbf{b}+\mathbf{c}}{2} \right)\] done
clear
C)
\[\mathbf{a}+\frac{\mathbf{b}+\mathbf{c}}{2}\] done
clear
D)
\[\frac{\mathbf{a}+\mathbf{b}+\mathbf{c}}{2}\] done
clear
View Solution play_arrow
-
question_answer61)
If in the given figure \[\overrightarrow{OA}=\mathbf{a},\,\,\,\overrightarrow{OB}=\mathbf{b}\] and \[AP\,\,:\,\,PB=m\,\,:\,\,n,\] then \[\overrightarrow{OP}=\] [RPET 1981; MP PET 1988]
A)
\[\frac{m\,\mathbf{a}+n\,\mathbf{b}}{m+n}\] done
clear
B)
\[\frac{n\,\mathbf{a}+m\,\mathbf{b}}{m+n}\] done
clear
C)
\[m\,\mathbf{a}-n\,\mathbf{b}\] done
clear
D)
\[\frac{m\,\mathbf{a}-n\,\mathbf{b}}{m-n}\] done
clear
View Solution play_arrow
-
question_answer62)
If D, E, F be the middle points of the sides BC, CA and AB of the triangle ABC, then \[\overrightarrow{AD}+\overrightarrow{BE}+\overrightarrow{CF}\] is
A)
A zero vector done
clear
B)
A unit vector done
clear
C)
0 done
clear
D)
None of these done
clear
View Solution play_arrow
-
question_answer63)
If a and b are the position vectors of A and B respectively, then the position vector of a point C on AB produced such that \[\overrightarrow{AC}=3\overrightarrow{AB}\] is [MNR 1980; MP PET 1995, 99]
A)
\[3\mathbf{a}-\mathbf{b}\] done
clear
B)
\[3\mathbf{b}-\mathbf{a}\] done
clear
C)
\[3\mathbf{a}-2\mathbf{b}\] done
clear
D)
\[3\mathbf{b}-2\mathbf{a}\] done
clear
View Solution play_arrow
-
question_answer64)
The position vectors of A and B are \[\mathbf{i}-\mathbf{j}+2\mathbf{k}\] and \[3\mathbf{i}-\mathbf{j}+3\mathbf{k}.\] The position vector of the middle point of the line AB is [MP PET 1988]
A)
\[\frac{1}{2}\mathbf{i}-\frac{1}{2}\mathbf{j}+\mathbf{k}\] done
clear
B)
\[2\mathbf{i}-\mathbf{j}+\frac{5}{2}\mathbf{k}\] done
clear
C)
\[\frac{3}{2}\mathbf{i}-\frac{1}{2}\mathbf{j}+\frac{3}{2}\mathbf{k}\] done
clear
D)
None of these done
clear
View Solution play_arrow
-
question_answer65)
If ABCD is a parallelogram and the position vectors of A, B, C are \[\mathbf{i}+3\mathbf{j}+5\mathbf{k},\,\,\mathbf{i}+\mathbf{j}+\mathbf{k}\] and \[7\mathbf{i}+7\mathbf{j}+7\mathbf{k},\] then the position vector of D will be
A)
\[7\mathbf{i}+5\mathbf{j}+3\mathbf{k}\] done
clear
B)
\[7\mathbf{i}+9\mathbf{j}+11\mathbf{k}\] done
clear
C)
\[9\mathbf{i}+11\mathbf{j}+13\mathbf{k}\] done
clear
D)
\[8\mathbf{i}+8\mathbf{j}+8\mathbf{k}\] done
clear
View Solution play_arrow
-
question_answer66)
P is the point of intersection of the diagonals of the parallelogram ABCD. If O is any point, then \[\overrightarrow{OA}+\overrightarrow{OB}+\overrightarrow{OC}+\overrightarrow{OD}=\] [RPET 1989; J & K 2005]
A)
\[\overrightarrow{OP}\] done
clear
B)
\[2\,\,\overrightarrow{OP}\] done
clear
C)
\[3\,\,\overrightarrow{OP}\] done
clear
D)
\[4\,\,\overrightarrow{OP}\] done
clear
View Solution play_arrow
-
question_answer67)
If the position vectors of the point A, B, C be i, j, k respectively and P be a point such that \[\overrightarrow{AB}=\overrightarrow{CP},\] then the position vector of P is
A)
\[-\mathbf{i}+\mathbf{j}+\mathbf{k}\] done
clear
B)
\[-\mathbf{i}-\mathbf{j}+\mathbf{k}\] done
clear
C)
\[\mathbf{i}+\mathbf{j}-\mathbf{k}\] done
clear
D)
None of these done
clear
View Solution play_arrow
-
question_answer68)
If the position vectors of the points A, B, C, D be \[2\mathbf{i}+3\mathbf{j}+5\mathbf{k},\] \[\mathbf{i}+2\mathbf{j}+3\mathbf{k},\,\,-5\mathbf{i}+4\mathbf{j}-2\mathbf{k}\] and \[\mathbf{i}+10\mathbf{j}+10\mathbf{k}\] respectively, then [MNR 1982]
A)
\[\overrightarrow{AB}=\overrightarrow{CD}\] done
clear
B)
\[\overrightarrow{AB}\,\,\,|\,\,|\,\,\,\overrightarrow{\,CD}\] done
clear
C)
\[\overrightarrow{AB}\,\,\bot \,\,\overrightarrow{CD}\] done
clear
D)
None of these done
clear
View Solution play_arrow
-
question_answer69)
If the position vector of one end of the line segment AB be \[2\mathbf{i}+3\mathbf{j}-\mathbf{k}\] and the position vector of its middle point be \[3\,(\mathbf{i}+\mathbf{j}+\mathbf{k}),\] then the position vector of the other end is
A)
\[4\mathbf{i}+3\mathbf{j}+5\mathbf{k}\] done
clear
B)
\[4\mathbf{i}-3\mathbf{j}+7\mathbf{k}\] done
clear
C)
\[4\mathbf{i}+3\mathbf{j}+7\mathbf{k}\] done
clear
D)
\[4\mathbf{i}+3\mathbf{j}-7\mathbf{k}\] done
clear
View Solution play_arrow
-
question_answer70)
If G and G' be the centroids of the triangles ABC and \[A'B'C'\] respectively, then \[\overrightarrow{AA}'+\overrightarrow{BB'}+\overrightarrow{CC}'=\]
A)
\[\frac{2}{3}\overrightarrow{GG}'\] done
clear
B)
\[\overrightarrow{GG}'\] done
clear
C)
\[2\,\overrightarrow{GG}'\] done
clear
D)
\[3\,\overrightarrow{GG}'\] done
clear
View Solution play_arrow
-
question_answer71)
If O be the circumcentre and O' be the orthocentre of the triangle ABC, then \[\overrightarrow{O'A}+\overrightarrow{O'B}+\overrightarrow{O'C}=\]
A)
\[\overrightarrow{OO}'\] done
clear
B)
\[2\,\overrightarrow{O'O}\] done
clear
C)
\[2\,\overrightarrow{OO'}\] done
clear
D)
0 done
clear
View Solution play_arrow
-
question_answer72)
If the vectors represented by the sides AB and BC of the regular hexagon ABCDEF be a and b, then the vector represented by \[\overrightarrow{AE}\] will be
A)
\[2\,\mathbf{b}-\mathbf{a}\] done
clear
B)
\[\mathbf{b}-\mathbf{a}\] done
clear
C)
\[2\,\mathbf{a}-\mathbf{b}\] done
clear
D)
\[\mathbf{a}+\mathbf{b}\] done
clear
View Solution play_arrow
-
question_answer73)
The position vector of a point C with respect to B is \[\mathbf{i}+\mathbf{j}\] and that of B with respect to A is \[\mathbf{i}-\mathbf{j}.\] The position vector of C with respect to A is [MP PET 1989]
A)
2 i done
clear
B)
2 j done
clear
C)
2 j done
clear
D)
2 i done
clear
View Solution play_arrow
-
question_answer74)
A and B are two points. The position vector of A is \[6\mathbf{b}-2\mathbf{a}.\] A point P divides the line AB in the ratio 1 : 2. If \[\mathbf{a}-\mathbf{b}\] is the position vector of P, then the position vector of B is given by [MP PET 1993]
A)
\[7\mathbf{a}-15\mathbf{b}\] done
clear
B)
\[7\mathbf{a}+15\mathbf{b}\] done
clear
C)
\[2\pi /3\] done
clear
D)
\[15\mathbf{a}+7\mathbf{b}\] done
clear
View Solution play_arrow
-
question_answer75)
If the position vectors of the points A and B are \[c=(2\,-2,\,4)\] and \[3\mathbf{i}-\mathbf{j}-3\mathbf{k},\] then what will be the position vector of the mid-point of AB [MP PET 1992]
A)
\[\mathbf{i}+2\mathbf{j}-\mathbf{k}\] done
clear
B)
\[2\mathbf{i}+\mathbf{j}-2\mathbf{k}\] done
clear
C)
\[2\mathbf{i}+\mathbf{j}-\mathbf{k}\] done
clear
D)
\[\mathbf{i}+\mathbf{j}-2\mathbf{k}\] done
clear
View Solution play_arrow
-
question_answer76)
If C is the middle point of AB and P is any point outside AB, then [MNR 1991; UPSEAT 2000; AIEEE 2005]
A)
\[\overrightarrow{PA}+\overrightarrow{PB}=\overrightarrow{PC}\] done
clear
B)
\[\overrightarrow{PA}+\overrightarrow{PB}=2\,\overrightarrow{PC}\] done
clear
C)
\[\overrightarrow{PA}+\overrightarrow{PB}+\overrightarrow{PC}=0\] done
clear
D)
\[\overrightarrow{PA}+\overrightarrow{PB}+2\,\overrightarrow{PC}=0\] done
clear
View Solution play_arrow
-
question_answer77)
If in a triangle \[\overrightarrow{AB}=\mathbf{a},\,\,\overrightarrow{AC}=\mathbf{b}\] and D, E are the mid-points of AB and AC respectively, then \[\overrightarrow{DE}\] is equal to [RPET 1986]
A)
\[\frac{\mathbf{a}}{4}-\frac{\mathbf{b}}{4}\] done
clear
B)
\[\frac{\mathbf{a}}{2}-\frac{\mathbf{b}}{2}\] done
clear
C)
\[\frac{\mathbf{b}}{4}-\frac{\mathbf{a}}{4}\] done
clear
D)
\[\frac{\mathbf{b}}{2}-\frac{\mathbf{a}}{2}\] done
clear
View Solution play_arrow
-
question_answer78)
In the triangle ABC, \[\overrightarrow{AB}=\mathbf{a},\,\,\overrightarrow{AC}=\mathbf{c},\,\,\overrightarrow{BC}=\mathbf{b}\], then [RPET 1984]
A)
\[\mathbf{a}+\mathbf{b}+\mathbf{c}=\mathbf{0}\] done
clear
B)
\[\mathbf{a}+\mathbf{b}-\mathbf{c}=\mathbf{0}\] done
clear
C)
\[\mathbf{a}-\mathbf{b}+\mathbf{c}=\mathbf{0}\] done
clear
D)
\[-\,\mathbf{a}+\mathbf{b}+\mathbf{c}=\mathbf{0}\] done
clear
View Solution play_arrow
-
question_answer79)
ABCDE is a pentagon. Forces \[\overrightarrow{AB},\,\overrightarrow{AE},\,\overrightarrow{DC},\,\overrightarrow{ED}\] act at a point. Which force should be added to this system to make the resultant \[{{\cos }^{-1}}\frac{4}{5}\] [MNR 1984]
A)
\[\overrightarrow{AC}\] done
clear
B)
\[\overrightarrow{AD}\] done
clear
C)
\[\overrightarrow{BC}\] done
clear
D)
\[\overrightarrow{BD}\] done
clear
View Solution play_arrow
-
question_answer80)
Let A and B be points with position vectors a and b with respect to the origin O. If the point C on OA is such that \[2AC=CO,\,\,CD\] is parallel to OB and \[|\overrightarrow{CD}|\,\,=\,\,3|\overrightarrow{OB}|,\] then \[\overrightarrow{AD}\] is equal to
A)
\[3\mathbf{b}-\frac{\mathbf{a}}{2}\] done
clear
B)
\[3\mathbf{b}+\frac{\mathbf{a}}{2}\] done
clear
C)
\[3\mathbf{b}-\frac{\mathbf{a}}{3}\] done
clear
D)
\[3\mathbf{b}+\frac{\mathbf{a}}{3}\] done
clear
View Solution play_arrow
-
question_answer81)
In a triangle ABC, if \[2\overrightarrow{AC}=3\overrightarrow{CB},\] then \[2\overrightarrow{OA}+3\overrightarrow{OB}\] equals [IIT 1988; Pb. CET 2003]
A)
\[5\overrightarrow{OC}\] done
clear
B)
\[\frac{1}{3}\,(2\mathbf{i}-2\mathbf{j}+\mathbf{k})\] done
clear
C)
\[\,\overrightarrow{OC}\] done
clear
D)
None of these done
clear
View Solution play_arrow
-
question_answer82)
If \[\overrightarrow{AO}+\overrightarrow{OB}=\overrightarrow{BO}+\overrightarrow{OC},\] then A, B, C form [IIT 1983]
A)
Equilateral triangle done
clear
B)
Right angled triangle done
clear
C)
Isosceles triangle done
clear
D)
Line done
clear
View Solution play_arrow
-
question_answer83)
The sum of the three vectors determined by the medians of a triangle directed from the vertices is [MP PET 1997]
A)
0 done
clear
B)
1 done
clear
C)
1 done
clear
D)
\[\frac{1}{3}\] done
clear
View Solution play_arrow
-
question_answer84)
The position vector of the points which divides internally in the ratio 2 : 3 the join of the points \[2\mathbf{a}-3\mathbf{b}\] and \[3\mathbf{a}-2\mathbf{b},\] is [AI CBSE 1985]
A)
\[\frac{12}{5}\mathbf{a}+\frac{13}{5}\mathbf{b}\] done
clear
B)
\[\frac{12}{5}\mathbf{a}-\frac{13}{5}\mathbf{b}\] done
clear
C)
\[\frac{3}{5}\mathbf{a}-\frac{2}{5}\mathbf{b}\] done
clear
D)
None of these done
clear
View Solution play_arrow
-
question_answer85)
If position vector of points A, B, C are respectively i, j, k and \[AB=CX,\] then position vector of point X is [MP PET 1994]
A)
\[-\,\mathbf{i}+\mathbf{j}+\mathbf{k}\] done
clear
B)
\[\mathbf{i}-\mathbf{j}+\mathbf{k}\] done
clear
C)
\[\mathbf{i}+\mathbf{j}-\mathbf{k}\] done
clear
D)
\[\mathbf{i}+\mathbf{j}+\mathbf{k}\] done
clear
View Solution play_arrow
-
question_answer86)
If a and b are P.V. of two points A and B and C divides AB in ratio 2 : 1, then P.V. of C is [RPET 1996]
A)
\[\frac{\mathbf{a}+2\mathbf{b}}{3}\] done
clear
B)
\[\frac{2\mathbf{a}+\mathbf{b}}{3}\] done
clear
C)
\[\frac{\mathbf{a}+2}{3}\] done
clear
D)
\[\frac{\mathbf{a}+\mathbf{b}}{2}\] done
clear
View Solution play_arrow
-
question_answer87)
If \[A,\,B,\,C\] are the vertices of a triangle whose position vectors are a, b, c and G is the centroid of the \[\Delta ABC,\] then \[\overrightarrow{GA}+\overrightarrow{GB}\,+\overrightarrow{GC}\] is [Karnataka CET 2000]
A)
0 done
clear
B)
\[\overrightarrow{A}+\overrightarrow{B}+\overrightarrow{C}\] done
clear
C)
\[\frac{\mathbf{a}+\mathbf{b}+\mathbf{c}}{3}\] done
clear
D)
\[\frac{\mathbf{a}+\mathbf{b}-\mathbf{c}}{3}\] done
clear
View Solution play_arrow
-
question_answer88)
If O is origin and C is the mid-point of \[A(2,\,\,-1)\] and \[B(-4,\,3)\]. Then value of \[\overrightarrow{OC}\] is [RPET 2001]
A)
i + j done
clear
B)
i ? j done
clear
C)
i + j done
clear
D)
i ? j done
clear
View Solution play_arrow
-
question_answer89)
If \[ABCDEF\] is regular hexagon, then \[\overrightarrow{AD}\,+\overrightarrow{EB}+\overrightarrow{FC}=\] [Karnataka CET 2002]
A)
0 done
clear
B)
\[2\overrightarrow{AB}\] done
clear
C)
\[3\overrightarrow{AB}\] done
clear
D)
\[4\overrightarrow{AB}\] done
clear
View Solution play_arrow
-
question_answer90)
If position vectors of a point A is a + 2b and a divides AB in the ratio \[2:3\], then the position vector of B is [MP PET 2002]
A)
2a ? b done
clear
B)
b ? 2a done
clear
C)
a ? 3b done
clear
D)
b done
clear
View Solution play_arrow
-
question_answer91)
If \[D,\,E,\,F\] are respectively the mid points of \[AB,\,AC\]and \[BC\] in \[\Delta ABC\], then \[\overrightarrow{BE}\]\[+\overrightarrow{AF}=\] [EAMCET 2003]
A)
\[\overrightarrow{DC}\] done
clear
B)
\[\frac{1}{2}\overrightarrow{BF}\] done
clear
C)
\[2\overrightarrow{BF}\] done
clear
D)
\[\frac{3}{2}\overrightarrow{BF}\] done
clear
View Solution play_arrow
-
question_answer92)
If \[4\mathbf{i}+7\mathbf{j}+8\mathbf{k},\,\,\,2\mathbf{i}+3\mathbf{j}+4\mathbf{k}\,\] and \[2\mathbf{i}+5\mathbf{j}+7\mathbf{k}\] are the position vectors of the vertices A, B and C respectively of triangle ABC. The position vector of the point where the bisector of angle A meets BC is [Pb. CET 2004]
A)
\[\frac{1}{3}\,(6\mathbf{i}+13\mathbf{j}+18\mathbf{k})\] done
clear
B)
\[\frac{2}{3}\,(6\mathbf{i}+12\mathbf{j}-8\mathbf{k})\] done
clear
C)
\[\frac{1}{3}\,(-6\mathbf{i}-8\mathbf{j}-9\mathbf{k})\] done
clear
D)
\[\frac{2}{3}\,(-6\mathbf{i}-12\mathbf{j}+8\mathbf{k})\] done
clear
View Solution play_arrow
-
question_answer93)
If \[\mathbf{a}=\mathbf{i}-\mathbf{j}\] and \[\mathbf{b}=\mathbf{i}+\mathbf{k}\], then a unit vector coplanar with a and b and perpendicular to a is
A)
i done
clear
B)
j done
clear
C)
k done
clear
D)
None of these done
clear
View Solution play_arrow
-
question_answer94)
If the position vectors of the points A, B, C be \[\mathbf{i}+\mathbf{j},\,\,\,\mathbf{i}-\mathbf{j}\] and \[a\,\,\mathbf{i}+b\,\mathbf{j}+c\,\mathbf{k}\] respectively, then the points A, B, C are collinear if
A)
\[a=b=c=1\] done
clear
B)
\[a=1,\,\,b\] and \[c\] are arbitrary scalars done
clear
C)
\[a=b=c=0\] done
clear
D)
\[c=0,\,\,a=1\] and b is arbitrary scalars done
clear
View Solution play_arrow
-
question_answer95)
If the points \[\mathbf{a}+\mathbf{b},\,\,\mathbf{a}-\mathbf{b}\] and \[\mathbf{a}+k\,\mathbf{b}\] be collinear, then k =
A)
0 done
clear
B)
2 done
clear
C)
2 done
clear
D)
Any real number done
clear
View Solution play_arrow
-
question_answer96)
If the position vectors of the points A, B, C be \[\mathbf{a},\ \mathbf{b}\], \[3\mathbf{a}-2\mathbf{b}\] respectively, then the points A, B, C are [MP PET 1989]
A)
Collinear done
clear
B)
Non-collinear done
clear
C)
Form a right angled triangle done
clear
D)
None of these done
clear
View Solution play_arrow
-
question_answer97)
If a, b, c are non-collinear vectors such that for some scalars x, y, z, \[x\mathbf{a}+y\mathbf{b}+z\mathbf{c}=\mathbf{0},\] then [RPET 2002]
A)
\[x=0,\,\,y=0,\,\,z=0\] done
clear
B)
\[x\ne 0,\,\,y\ne 0,\,\,z=0\] done
clear
C)
\[x=0,\,\,y\ne 0,\,\,z\ne 0\] done
clear
D)
\[x\ne 0,\,\,y\ne 0,\,\,z\ne 0\] done
clear
View Solution play_arrow
-
question_answer98)
The vectors \[3\,\mathbf{i}+\mathbf{j}-5\,\mathbf{k}\] and \[a\,\mathbf{i}+b\,\mathbf{j}-15\,\mathbf{k}\]are collinear, if [RPET 1986; MP PET 1988]
A)
\[a=3,\,\,b=1\] done
clear
B)
\[a=9,\,\,b=1\] done
clear
C)
\[a=3,\,\,b=3\] done
clear
D)
\[a=9,\,\,b=3\] done
clear
View Solution play_arrow
-
question_answer99)
The points with position vectors \[60\,\mathbf{i}+3\,\mathbf{j}\], \[40\,\mathbf{i}-8\mathbf{j},\], \[a\,\mathbf{i}-52\,\mathbf{j}\] are collinear, if \[a=\] [RPET 1991; IIT 1983; MP PET 2002]
A)
40 done
clear
B)
40 done
clear
C)
20 done
clear
D)
None of these done
clear
View Solution play_arrow
-
question_answer100)
If O be the origin and the position vector of A be \[4\,\mathbf{i}+5\,\mathbf{j},\] then a unit vector parallel to \[\overrightarrow{OA}\] is
A)
\[\frac{4}{\sqrt{41}}\mathbf{i}\] done
clear
B)
\[\frac{5}{\sqrt{41}}\mathbf{i}\] done
clear
C)
\[\frac{1}{\sqrt{41}}(4\,\mathbf{i}+5\,\mathbf{j})\] done
clear
D)
\[\frac{1}{\sqrt{41}}(4\,\mathbf{i}-5\,\mathbf{j})\] done
clear
View Solution play_arrow
-
question_answer101)
If the position vectors of the points A and B be \[2\,\mathbf{i}+3\,\mathbf{j}-\mathbf{k}\] and \[-2\,\mathbf{i}+3\,\mathbf{j}+4\,\mathbf{k},\] then the line AB is parallel to
A)
xy-plane done
clear
B)
yz-plane done
clear
C)
zx-plane done
clear
D)
None of these done
clear
View Solution play_arrow
-
question_answer102)
The points with position vectors \[10\,\mathbf{i}+3\,\mathbf{j},\,\,12\,\mathbf{i}-5\,\mathbf{j}\] and \[a\,\mathbf{i}+11\,\mathbf{j}\] are collinear, if \[a=\] [MNR 1992; Kurukshetra CEE 2002]
A)
8 done
clear
B)
4 done
clear
C)
8 done
clear
D)
12 done
clear
View Solution play_arrow
-
question_answer103)
Three points whose position vectors are \[\mathbf{a}+\mathbf{b},\,\,\mathbf{a}-\mathbf{b}\] and \[\mathbf{a}+k\mathbf{b}\] will be collinear, if the value of k is [IIT 1984]
A)
Zero done
clear
B)
Only negative real number done
clear
C)
Only positive real number done
clear
D)
Every real number done
clear
View Solution play_arrow
-
question_answer104)
If the position vectors of A, B, C, D are \[2\,\mathbf{i}+\mathbf{j},\] \[\mathbf{i}-3\,\mathbf{j},\] \[3\,\mathbf{i}+2\,\mathbf{j}\] and \[\mathbf{i}+\lambda \mathbf{j}\] respectively and \[\overrightarrow{AB}||\overrightarrow{CD}\] , then \[\lambda \] will be [RPET 1988]
A)
8 done
clear
B)
6 done
clear
C)
8 done
clear
D)
6 done
clear
View Solution play_arrow
-
question_answer105)
If the vectors \[3\,\mathbf{i}+2\,\mathbf{j}-\mathbf{k}\]and \[6\,\mathbf{i}-4x\mathbf{j}+y\mathbf{k}\] are parallel, then the value of x and y will be [RPET 1985, 86]
A)
1, ? 2 done
clear
B)
1, ? 2 done
clear
C)
1, 2 done
clear
D)
1, 2 done
clear
View Solution play_arrow
-
question_answer106)
If \[(x,\,\,y,\,\,z)\ne (0,\,\,0,\,\,0)\] and \[(\mathbf{i}+\mathbf{j}+3\,\mathbf{k})\,x+(3\,\mathbf{i}-3\mathbf{j}+\mathbf{k})\,y\]\[+(-4\mathbf{i}+5\mathbf{j})\,z=\lambda \,(x\mathbf{i}+y\mathbf{j}+z\mathbf{k}),\] then the value of l will be [IIT 1982; RPET 1984]
A)
2, 0 done
clear
B)
0, ? 2 done
clear
C)
1, 0 done
clear
D)
0, ? 1 done
clear
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question_answer107)
The vectors a, b and a + b are
A)
Collinear done
clear
B)
Coplanar done
clear
C)
Non-coplanar done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer108)
If a, b, c are the position vectors of three collinear points, then the existence of x, y, z is such that
A)
\[x\mathbf{a}+y\mathbf{b}+z\mathbf{c}=0,\,\,x+y+z\ne 0\] done
clear
B)
\[x\mathbf{a}+y\mathbf{b}+z\mathbf{c}\ne 0,\,\,x+y+z=0\] done
clear
C)
\[x\mathbf{a}+y\mathbf{b}+z\mathbf{c}\ne 0,\,\,x+y+z\ne 0\] done
clear
D)
\[x\mathbf{a}+y\mathbf{b}+z\mathbf{c}=0,\,\,x+y+z=0\] done
clear
View Solution play_arrow
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question_answer109)
If \[\mathbf{a}=(2,\,\,5)\] and \[\mathbf{b}=(1,\,\,4),\] then the vector parallel to \[(\mathbf{a}+\mathbf{b})\] is
A)
(3, 5) done
clear
B)
(1, 1) done
clear
C)
(1, 3) done
clear
D)
(8, 5) done
clear
View Solution play_arrow
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question_answer110)
The vectors a and b are non-collinear. The value of x for which the vectors \[\mathbf{c}=(x-2)\,\mathbf{a}+\mathbf{b}\] and \[\mathbf{d}=(2x+1)\,\mathbf{a}-\mathbf{b}\] are collinear, is
A)
1 done
clear
B)
\[\frac{1}{2}\] done
clear
C)
\[\frac{1}{3}\] done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer111)
sThe vectors \[\mathbf{i}+2\mathbf{j}+3\mathbf{k},\] \[\lambda \mathbf{i}+4\mathbf{j}+7\mathbf{k},\] \[-3\mathbf{i}-2\mathbf{j}-5\mathbf{k}\] are collinear, if l equals [Kurukshetra CEE 1996]
A)
3 done
clear
B)
4 done
clear
C)
5 done
clear
D)
6 done
clear
View Solution play_arrow
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question_answer112)
The position vectors of four points P, Q, R, S are \[2\mathbf{a}+4\mathbf{c},\,\] \[5\mathbf{a}+3\sqrt{3}\,\mathbf{b}+4\mathbf{c},\] \[-2\sqrt{3}\mathbf{b}+\mathbf{c}\] and \[2\mathbf{a}+\mathbf{c}\] respectively, then [MP PET 1997]
A)
\[\overrightarrow{PQ}\] is parallel to \[\overrightarrow{RS}\] done
clear
B)
\[\overrightarrow{PQ}\] is not parallel to \[\overrightarrow{RS}\] done
clear
C)
\[\overrightarrow{PQ}\] is equal to \[\overrightarrow{RS}\] done
clear
D)
\[\overrightarrow{PQ}\] is parallel and equal to \[\overrightarrow{RS}\] done
clear
View Solution play_arrow
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question_answer113)
If \[\mathbf{a}=(1,\,\,-1)\] and \[\mathbf{b}=(-\,2,\,m)\] are two collinear vectors, then m= [MP PET 1998]
A)
4 done
clear
B)
3 done
clear
C)
2 done
clear
D)
0 done
clear
View Solution play_arrow
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question_answer114)
If three points A, B, C are collinear, whose position vectors are \[\mathbf{i}-2\mathbf{j}-8\mathbf{k},\,\,5\mathbf{i}-2\mathbf{k}\] and \[11\,\mathbf{i}+\,3\,\mathbf{j}+7\mathbf{k}\] respectively, then the ratio in which B divides AC is [RPET 1999]
A)
1 : 2 done
clear
B)
2 : 3 done
clear
C)
2 : 1 done
clear
D)
1 : 1 done
clear
View Solution play_arrow
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question_answer115)
If a and b are two non-collinear vectors and \[x\,\mathbf{a}+y\,\mathbf{b}=0\] [RPET 2001]
A)
\[x=0\], but y is not necessarily zero done
clear
B)
\[y=0\], but x is not necessarily zero done
clear
C)
\[x=0\], \[y=0\] done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer116)
If three points A, B and C have position vectors \[(1,\,x,\,3),\,\,(3,\,4,\,7)\] and \[ap+bq+cr=1\] respectively and if they are collinear, then \[(x,\,y)=\] [EAMCET 2002]
A)
(2, ? 3) done
clear
B)
(? 2, 3) done
clear
C)
(2, 3) done
clear
D)
(? 2, ? 3) done
clear
View Solution play_arrow
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question_answer117)
a and b are two non-collinear vectors, then \[x\mathbf{a}+y\mathbf{b}\] (where x and y are scalars) represents a vector which is [MP PET 2003]
A)
Parallel to b done
clear
B)
Parallel to a done
clear
C)
Coplanar with a and b done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer118)
If a, b, c are three non-coplanar vectors such that \[\mathbf{a}+\mathbf{b}+\mathbf{c}=\alpha \,\mathbf{d}\] and \[\mathbf{b}+\mathbf{c}+\mathbf{d}=\beta \,\mathbf{a},\] then \[\mathbf{a}+\mathbf{b}+\mathbf{c}+\mathbf{d}\] is equal to
A)
0 done
clear
B)
\[\alpha \text{ }\mathbf{a}\] done
clear
C)
\[\beta \text{ }\mathbf{b}\] done
clear
D)
\[(\alpha +\beta )\,\mathbf{c}\] done
clear
View Solution play_arrow
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question_answer119)
The value of k for which the vectors \[\mathbf{a}=\mathbf{i}-\mathbf{j}\] and \[\mathbf{b}=-2\,\mathbf{i}+k\,\mathbf{j}\] are collinear is [Pb. CET 2004]
A)
2 done
clear
B)
\[\frac{1}{2}\] done
clear
C)
\[\frac{1}{3}\] done
clear
D)
3 done
clear
View Solution play_arrow