
The vector projection of a vector \[3\hat{i}+4\hat{k}\]on yaxis is [RPMT 2004]
A)
5 done
clear
B)
4 done
clear
C)
3 done
clear
D)
Zero done
clear
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Position of a particle in a rectangularcoordinate system is (3, 2, 5). Then its position vector will be
A)
\[3\hat{i}+5\hat{j}+2\hat{k}\] done
clear
B)
\[3\hat{i}+2\hat{j}+5\hat{k}\] done
clear
C)
\[5\hat{i}+3\hat{j}+2\hat{k}\] done
clear
D)
None of these done
clear
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If a particle moves from point P (2, 3, 5) to point Q (3,4,5). Its displacement vector be
A)
\[\hat{i}+\hat{j}+10\hat{k}\] done
clear
B)
\[\hat{i}+\hat{j}+5\hat{k}\] done
clear
C)
\[\hat{i}+\hat{j}\] done
clear
D)
\[2\hat{i}+4\hat{j}+6\hat{k}\] done
clear
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A force of 5 N acts on a particle along a direction making an angle of 60? with vertical. Its vertical component be
A)
10 N done
clear
B)
3 N done
clear
C)
4 N done
clear
D)
2.5 N done
clear
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If \[A=3\hat{i}+4\hat{j}\] and \[B=7\hat{i}+24\hat{j},\]the vector having the same magnitude as B and parallel to A is
A)
\[5\hat{i}+20\hat{j}\] done
clear
B)
\[15\hat{i}+10\hat{j}\] done
clear
C)
\[20\hat{i}+15\hat{j}\] done
clear
D)
\[15\hat{i}+20\hat{j}\] done
clear
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Vector\[\overrightarrow{A}\] makes equal angles with x, y and z axis. Value of its components (in terms of magnitude of \[\overrightarrow{A}\]) will be
A)
\[\frac{A}{\sqrt{3}}\] done
clear
B)
\[\frac{A}{\sqrt{2}}\] done
clear
C)
\[\sqrt{3}\,A\] done
clear
D)
\[\frac{\sqrt{3}}{A}\] done
clear
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If \[\overrightarrow{A}=2\hat{i}+4\hat{j}5\hat{k}\] the direction of cosines of the vector \[\overrightarrow{A}\] are
A)
\[\frac{2}{\sqrt{45}},\frac{4}{\sqrt{45}}\,\text{and}\,\frac{\,\text{5}}{\sqrt{\text{45}}}\] done
clear
B)
\[\frac{1}{\sqrt{45}},\frac{2}{\sqrt{45}}\,\text{and}\,\frac{\text{3}}{\sqrt{\text{45}}}\] done
clear
C)
\[\frac{4}{\sqrt{45}},\,0\,\text{and}\,\frac{\text{4}}{\sqrt{45}}\] done
clear
D)
\[\frac{3}{\sqrt{45}},\frac{2}{\sqrt{45}}\,\text{and}\,\frac{\text{5}}{\sqrt{\text{45}}}\] done
clear
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The vector that must be added to the vector \[\hat{i}3\hat{j}+2\hat{k}\] and \[3\hat{i}+6\hat{j}7\hat{k}\] so that the resultant vector is a unit vector along the yaxis is
A)
\[4\hat{i}+2\hat{j}+5\hat{k}\] done
clear
B)
\[4\hat{i}2\hat{j}+5\hat{k}\] done
clear
C)
\[3\hat{i}+4\hat{j}+5\hat{k}\] done
clear
D)
Null vector done
clear
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How many minimum number of coplanar vectors having different magnitudes can be added to give zero resultant
A)
2 done
clear
B)
3 done
clear
C)
4 done
clear
D)
5 done
clear
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A hall has the dimensions \[10\,m\times 12\,m\times 14\,m.\]A fly starting at one corner ends up at a diametrically opposite corner. What is the magnitude of its displacement
A)
17 m done
clear
B)
26 m done
clear
C)
36 m done
clear
D)
20 m done
clear
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100 coplanar forces each equal to 10 N act on a body. Each force makes angle \[\pi /50\]with the preceding force. What is the resultant of the forces
A)
1000 N done
clear
B)
500 N done
clear
C)
250 N done
clear
D)
Zero done
clear
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The magnitude of a given vector with end points (4, ? 4, 0) and (? 2, ? 2, 0) must be
A)
6 done
clear
B)
\[5\sqrt{2}\] done
clear
C)
4 done
clear
D)
\[2\sqrt{10}\] done
clear
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The expression \[\left( \frac{1}{\sqrt{2}}\hat{i}+\frac{1}{\sqrt{2}}\hat{j} \right)\] is a
A)
Unit vector done
clear
B)
Null vector done
clear
C)
Vector of magnitude \[\sqrt{2}\] done
clear
D)
Scalar done
clear
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Given vector \[\overrightarrow{A}=2\hat{i}+3\hat{j},\]the angle between \[\overrightarrow{A}\]and yaxis is [CPMT 1993]
A)
\[{{\tan }^{1}}3/2\] done
clear
B)
\[{{\tan }^{1}}2/3\] done
clear
C)
\[{{\sin }^{1}}2/3\] done
clear
D)
\[{{\cos }^{1}}2/3\] done
clear
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The unit vector along \[\hat{i}+\hat{j}\] is
A)
\[\hat{k}\] done
clear
B)
\[\hat{i}+\hat{j}\] done
clear
C)
\[\frac{\hat{i}+\hat{j}}{\sqrt{2}}\] done
clear
D)
\[\frac{\hat{i}+\hat{j}}{2}\] done
clear
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A vector is represented by \[3\,\hat{i}+\hat{j}+2\,\hat{k}\]. Its length in XY plane is [EAMCET (Engg.) 1994]
A)
2 done
clear
B)
\[\sqrt{14}\] done
clear
C)
\[\sqrt{10}\] done
clear
D)
\[\sqrt{5}\] done
clear
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Five equal forces of 10 N each are applied at one point and all are lying in one plane. If the angles between them are equal, the resultant force will be [CBSE PMT 1995]
A)
Zero done
clear
B)
10 N done
clear
C)
20 N done
clear
D)
\[10\sqrt{2}N\] done
clear
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The angle made by the vector \[A=\hat{i}+\hat{j}\] with x axis is [EAMCET (Engg.) 1999]
A)
\[\text{9}0{}^\circ \] done
clear
B)
\[\text{45}{}^\circ \] done
clear
C)
\[\text{22}.\text{5}{}^\circ \] done
clear
D)
\[\text{3}0{}^\circ \] done
clear
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Any vector in an arbitrary direction can always be replaced by two (or three)
A)
Parallel vectors which have the original vector as their resultant done
clear
B)
Mutually perpendicular vectors which have the original vector as their resultant done
clear
C)
Arbitrary vectors which have the original vector as their resultant done
clear
D)
It is not possible to resolve a vector done
clear
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Angular momentum is [MNR 1986]
A)
A scalar done
clear
B)
A polar vector done
clear
C)
An axial vector done
clear
D)
None of these done
clear
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Which of the following is a vector
A)
Pressure done
clear
B)
Surface tension done
clear
C)
Moment of inertia done
clear
D)
None of these done
clear
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If \[\vec{P}=\vec{Q}\]then which of the following is NOT correct
A)
\[\hat{P}=\hat{Q}\] done
clear
B)
\[\,\vec{P}\,\,=\,\,\vec{Q}\,\] done
clear
C)
\[P\hat{Q}=Q\hat{P}\] done
clear
D)
\[\vec{P}+\vec{Q}=\hat{P}+\hat{Q}\] done
clear
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The position vector of a particle is \[\vec{r}=(a\cos \omega t)\hat{i}+(a\sin \omega t)\hat{j}\]. The velocity of the particle is [CBSE PMT 1995]
A)
Parallel to the position vector done
clear
B)
Perpendicular to the position vector done
clear
C)
Directed towards the origin done
clear
D)
Directed away from the origin done
clear
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Which of the following is a scalar quantity [AFMC 1998]
A)
Displacement done
clear
B)
Electric field done
clear
C)
Acceleration done
clear
D)
Work done
clear
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If a unit vector is represented by \[0.5\hat{i}+0.8\hat{j}+c\hat{k}\], then the value of ?c? is [CBSE PMT 1999; EAMCET 1994]
A)
1 done
clear
B)
\[\sqrt{0.11}\] done
clear
C)
\[\sqrt{0.01}\] done
clear
D)
\[\sqrt{0.39}\] done
clear
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A boy walks uniformally along the sides of a rectangular park of size 400 mx 300 m, starting from one corner to the other corner diagonally opposite. Which of the following statement is incorrect [HP PMT 1999]
A)
He has travelled a distance of 700 m done
clear
B)
His displacement is 700 m done
clear
C)
His displacement is 500 m done
clear
D)
His velocity is not uniform throughout the walk done
clear
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The unit vector parallel to the resultant of the vectors \[\vec{A}=4\hat{i}+3\hat{j}+6\hat{k}\] and \[\vec{B}=\hat{i}+3\hat{j}8\hat{k}\] is [EAMCET 2000]
A)
\[\frac{1}{7}(3\hat{i}+6\hat{j}2\hat{k})\] done
clear
B)
\[\frac{1}{7}(3\hat{i}+6\hat{j}+2\hat{k})\] done
clear
C)
\[\frac{1}{49}(3\hat{i}+6\hat{j}2\hat{k})\] done
clear
D)
\[\frac{1}{49}(3\hat{i}6\hat{j}+2\hat{k})\] done
clear
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Surface area is [J&K CET 2002]
A)
Scalar done
clear
B)
Vector done
clear
C)
Neither scalar nor vector done
clear
D)
Both scalar and vector done
clear
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With respect to a rectangular cartesian coordinate system, three vectors are expressed as \[\vec{a}=4\hat{i}\hat{j}\], \[\vec{b}=3\hat{i}+2\hat{j}\] and \[\vec{c}=\hat{k}\] where \[\hat{i},\,\hat{j},\,\hat{k}\]are unit vectors, along the X, Y and Zaxis respectively. The unit vectors \[\hat{r}\]along the direction of sum of these vector is [Kerala CET (Engg.) 2003]
A)
\[\hat{r}=\frac{1}{\sqrt{3}}(\hat{i}+\hat{j}\hat{k})\] done
clear
B)
\[\hat{r}=\frac{1}{\sqrt{2}}(\hat{i}+\hat{j}\hat{k})\] done
clear
C)
\[\hat{r}=\frac{1}{3}(\hat{i}\hat{j}+\hat{k})\] done
clear
D)
\[\hat{r}=\frac{1}{\sqrt{2}}(\hat{i}+\hat{j}+\hat{k})\] done
clear
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The angle between the two vectors\[\vec{A}=3\hat{i}+4\hat{j}+5\hat{k}\]and \[\vec{B}=3\hat{i}+4\hat{j}+5\hat{k}\] is [DPMT 2000]
A)
60? done
clear
B)
Zero done
clear
C)
90? done
clear
D)
None of these done
clear
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The position vector of a particle is determined by the expression \[\vec{r}=3{{t}^{2}}\hat{i}+4{{t}^{2}}\hat{j}+7\hat{k}\] The distance traversed in first 10 sec is [DPMT 2002]
A)
500 m done
clear
B)
300 m done
clear
C)
150 m done
clear
D)
100 m done
clear
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Unit vector parallel to the resultant of vectors \[\vec{A}=4\hat{i}3\hat{j}\]and \[\vec{B}=8\hat{i}+8\hat{j}\]will be [BHU 1995]
A)
\[\frac{24\hat{i}+5\hat{j}}{13}\] done
clear
B)
\[\frac{12\hat{i}+5\hat{j}}{13}\] done
clear
C)
\[\frac{6\hat{i}+5\hat{j}}{13}\] done
clear
D)
None of these done
clear
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The component of vector \[A=2\hat{i}+3\hat{j}\]along the vector \[\hat{i}+\hat{j}\]is [KCET 1997]
A)
\[\frac{5}{\sqrt{2}}\] done
clear
B)
\[10\sqrt{2}\] done
clear
C)
\[5\sqrt{2}\] done
clear
D)
5 done
clear
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The angle between the two vectors \[\vec{A}=3\hat{i}+4\hat{j}+5\hat{k}\] and \[\vec{B}=3\hat{i}+4\hat{j}5\hat{k}\] will be [Pb. CET 2001]
A)
\[\text{9}0{}^\circ \] done
clear
B)
\[0{}^\circ \] done
clear
C)
\[\text{6}0{}^\circ \] done
clear
D)
\[\text{45}{}^\circ \] done
clear
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