-
question_answer1)
If a vector \[2\hat{i}+3\hat{j}+8\hat{k}\]is perpendicular to the vector \[4\hat{j}-4\hat{i}+\alpha \hat{k}\]. Then the value of \[\alpha \] is [CBSE PMT 2005]
A)
?1 done
clear
B)
\[\frac{1}{2}\] done
clear
C)
\[-\frac{1}{2}\] done
clear
D)
1 done
clear
View Solution play_arrow
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question_answer2)
If two vectors \[2\hat{i}+3\hat{j}-\hat{k}\] and \[-4\hat{i}-6\hat{j}-\lambda \hat{k}\] are parallel to each other then value of l be
A)
0 done
clear
B)
2 done
clear
C)
3 done
clear
D)
4 done
clear
View Solution play_arrow
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question_answer3)
A body, acted upon by a force of 50 N is displaced through a distance 10 meter in a direction making an angle of 60° with the force. The work done by the force be
A)
200 J done
clear
B)
100 J done
clear
C)
300 done
clear
D)
250 J done
clear
View Solution play_arrow
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question_answer4)
A particle moves from position \[3\hat{i}+2\hat{j}-6\hat{k}\] to \[14\hat{i}+13\hat{j}+9\hat{k}\] due to a uniform force of \[(4\hat{i}+\hat{j}+3\hat{k})\,N.\] If the displacement in meters then work done will be [CMEET 1995; Pb. PMT 2002, 03]
A)
100 J done
clear
B)
200 J done
clear
C)
300 J done
clear
D)
250 J done
clear
View Solution play_arrow
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question_answer5)
If for two vector \[\overrightarrow{A}\] and \[\overrightarrow{B}\], sum \[(\overrightarrow{A}+\overrightarrow{B})\] is perpendicular to the difference \[(\overrightarrow{A}-\overrightarrow{B})\]. The ratio of their magnitude is
A)
1 done
clear
B)
2 done
clear
C)
3 done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer6)
The angle between the vectors \[\overrightarrow{A}\] and \[\overrightarrow{B}\] is \[\theta .\]The value of the triple product \[\overrightarrow{A}\,.\,(\overrightarrow{B}\times \overrightarrow{A}\,)\] is [CBSE PMT 1991, 2005]
A)
\[{{A}^{2}}B\] done
clear
B)
Zero done
clear
C)
\[{{A}^{2}}B\sin \theta \] done
clear
D)
\[{{A}^{2}}B\cos \theta \] done
clear
View Solution play_arrow
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question_answer7)
If \[\overset{\to }{\mathop{A}}\,\,\times \,\overset{\to }{\mathop{B}}\,\,=\,\overset{\to }{\mathop{B}}\,\,\times \,\overset{\to }{\mathop{A}}\,\] then the angle between A and B is [AIEEE 2004]
A)
p / 2\[\] done
clear
B)
p / 3 done
clear
C)
p done
clear
D)
p / 4 done
clear
View Solution play_arrow
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question_answer8)
If \[\overrightarrow{A}=3\hat{i}+\hat{j}+2\hat{k}\] and \[\overrightarrow{B}=2\hat{i}-2\hat{j}+4\hat{k}\] then value of \[|\overrightarrow{A}\times \overrightarrow{B}|\,\] will be
A)
\[8\sqrt{2}\] done
clear
B)
\[8\sqrt{3}\] done
clear
C)
\[8\sqrt{5}\] done
clear
D)
\[5\sqrt{8}\] done
clear
View Solution play_arrow
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question_answer9)
The torque of the force \[\overrightarrow{F}=(2\hat{i}-3\hat{j}+4\hat{k}\,)N\] acting at the point \[\overrightarrow{r\,}=(3\hat{i}+2\hat{j}+3\hat{k})\]m about the origin be [CBSE PMT 1995]
A)
\[6\hat{i}-6\hat{j}+12\hat{k}\] done
clear
B)
\[17\hat{i}-6\hat{j}-13\hat{k}\] done
clear
C)
\[-6\hat{i}+6\hat{j}-12\hat{k}\] done
clear
D)
\[-17\hat{i}+6\hat{j}+13\hat{k}\] done
clear
View Solution play_arrow
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question_answer10)
If \[\overrightarrow{A}\times \overrightarrow{B}=\overrightarrow{C},\]then which of the following statements is wrong
A)
\[\overrightarrow{C}\,\bot \,\overrightarrow{A}\] done
clear
B)
\[\overrightarrow{C}\,\bot \,\overrightarrow{B}\] done
clear
C)
\[\overrightarrow{C}\,\bot \,(\overrightarrow{A}+\overrightarrow{B})\] done
clear
D)
\[\overrightarrow{C}\,\bot \,(\overrightarrow{A}\times \overrightarrow{B})\] done
clear
View Solution play_arrow
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question_answer11)
If a particle of mass m is moving with constant velocity v parallel to x-axis in x-y plane as shown in fig. Its angular momentum with respect to origin at any time t will be
A)
\[mvb\,\hat{k}\] done
clear
B)
\[-mvb\,\hat{k}\] done
clear
C)
\[mvb\,\hat{i}\] done
clear
D)
\[mv\,\hat{i}\] done
clear
View Solution play_arrow
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question_answer12)
Consider two vectors \[{{\overrightarrow{F}}_{1}}=2\hat{i}+5\hat{k}\] and \[{{\overrightarrow{F}}_{2}}=3\hat{j}+4\hat{k}.\] The magnitude of the scalar product of these vectors is [MP PMT 1987]
A)
20 done
clear
B)
23 done
clear
C)
\[5\sqrt{33}\] done
clear
D)
26 done
clear
View Solution play_arrow
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question_answer13)
Consider a vector \[\overrightarrow{F}=4\hat{i}-3\hat{j}.\]Another vector that is perpendicular to \[\overrightarrow{F}\] is
A)
\[4\hat{i}+3\hat{j}\] done
clear
B)
\[6\hat{i}\] done
clear
C)
\[7\hat{k}\] done
clear
D)
\[3\hat{i}-4\hat{j}\] done
clear
View Solution play_arrow
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question_answer14)
Two vectors \[\overrightarrow{A}\] and \[\overrightarrow{B}\] are at right angles to each other, when [AIIMS 1987]
A)
\[\overrightarrow{A}+\overrightarrow{B}=0\] done
clear
B)
\[\overrightarrow{A}-\overrightarrow{B}=0\] done
clear
C)
\[\overrightarrow{A}\times \overrightarrow{B}=0\] done
clear
D)
\[\overrightarrow{A}\,.\,\overrightarrow{B}=0\] done
clear
View Solution play_arrow
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question_answer15)
If \[|{{\overrightarrow{V}}_{1}}+{{\overrightarrow{V}}_{2}}|\,=\,|{{\overrightarrow{V}}_{1}}-{{\overrightarrow{V}}_{2}}|\]and \[{{V}_{2}}\] is finite, then [CPMT 1989]
A)
\[{{V}_{1}}\] is parallel to \[{{V}_{2}}\] done
clear
B)
\[{{\overrightarrow{V}}_{1}}={{\overrightarrow{V}}_{2}}\] done
clear
C)
\[{{V}_{1}}\] and \[{{V}_{2}}\] are mutually perpendicular done
clear
D)
\[|{{\overrightarrow{V}}_{1}}|\,=\,|{{\overrightarrow{V}}_{2}}|\] done
clear
View Solution play_arrow
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question_answer16)
A force \[\overrightarrow{F}=(5\hat{i}+3\hat{j})\]Newton is applied over a particle which displaces it from its origin to the point \[\overrightarrow{r}=(2\hat{i}-1\hat{j})\] metres. The work done on the particle is [MP PMT 1995]
A)
? 7 J done
clear
B)
+13 J done
clear
C)
+7 J done
clear
D)
+11 J done
clear
View Solution play_arrow
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question_answer17)
The angle between two vectors \[-2\hat{i}+3\hat{j}+\hat{k}\] and \[\hat{i}+2\hat{j}-4\hat{k}\] is [EAMCET 1990]
A)
0° done
clear
B)
90° done
clear
C)
180° done
clear
D)
None of the above done
clear
View Solution play_arrow
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question_answer18)
The angle between the vectors \[(\hat{i}+\hat{j})\] and \[(\hat{j}+\hat{k})\] is [EAMCET 1995]
A)
30° done
clear
B)
45° done
clear
C)
60° done
clear
D)
90° done
clear
View Solution play_arrow
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question_answer19)
A particle moves with a velocity \[6\hat{i}-4\hat{j}+3\hat{k}\,m/s\]under the influence of a constant force \[\overrightarrow{F}=20\hat{i}+15\hat{j}-5\hat{k}\,N.\,\]The instantaneous power applied to the particle is [CBSE PMT 2000]
A)
35 J/s done
clear
B)
45 J/s done
clear
C)
25 J/s done
clear
D)
195 J/s done
clear
View Solution play_arrow
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question_answer20)
If \[\overrightarrow{P}.\overrightarrow{Q}=PQ,\]then angle between \[\overrightarrow{P}\]and \[\overrightarrow{Q}\] is [AIIMS 1999]
A)
0° done
clear
B)
30° done
clear
C)
45° done
clear
D)
60° done
clear
View Solution play_arrow
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question_answer21)
A force \[\overrightarrow{\text{F}}=5\hat{i}+6\hat{j}+4\hat{k}\] acting on a body, produces a displacement \[\overrightarrow{\text{S}}=6\hat{i}-5\hat{k}.\]Work done by the force is [KCET 1999]
A)
10 units done
clear
B)
18 units done
clear
C)
11 units done
clear
D)
5 units done
clear
View Solution play_arrow
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question_answer22)
The angle between the two vectors \[\overrightarrow{A}=5\hat{i}+5\hat{j}\] and \[\overrightarrow{B}=5\hat{i}-5\hat{j}\]will be [CPMT 2000]
A)
Zero done
clear
B)
\[45{}^\circ \] done
clear
C)
\[90{}^\circ \] done
clear
D)
\[180{}^\circ \] done
clear
View Solution play_arrow
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question_answer23)
The vector \[\overrightarrow{P}=a\hat{i}+a\hat{j}+3\hat{k}\] and \[\overrightarrow{Q}=a\hat{i}-2\hat{j}-\hat{k}\] are perpendicular to each other. The positive value of a is [AFMC 2000; AIIMS 2002]
A)
3 done
clear
B)
4 done
clear
C)
9 done
clear
D)
13 done
clear
View Solution play_arrow
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question_answer24)
A body, constrained to move in the Y-direction is subjected to a force given by \[\overrightarrow{F}=(-2\hat{i}+15\hat{j}+6\hat{k})\,N.\] What is the work done by this force in moving the body a distance 10 m along the Y-axis [CBSE PMT 1994]
A)
20 J done
clear
B)
150 J done
clear
C)
160 J done
clear
D)
190 J done
clear
View Solution play_arrow
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question_answer25)
A particle moves in the x-y plane under the action of a force \[\overrightarrow{F}\] such that the value of its linear momentum \[(\overrightarrow{P})\] at anytime t is \[{{P}_{x}}=2\cos t,\,{{p}_{y}}=2\sin t.\]The angle \[\theta \]between \[\overrightarrow{F}\] and \[\overrightarrow{P}\] at a given time t. will be [MNR 1991; UPSEAT 2000]
A)
\[\theta =0{}^\circ \] done
clear
B)
\[\theta =30{}^\circ \] done
clear
C)
\[\theta =90{}^\circ \] done
clear
D)
\[\theta =180{}^\circ \] done
clear
View Solution play_arrow
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question_answer26)
The area of the parallelogram represented by the vectors \[\overrightarrow{A}=2\hat{i}+3\hat{j}\] and \[\overrightarrow{B}=\hat{i}+4\hat{j}\] is
A)
14 units done
clear
B)
7.5 units done
clear
C)
10 units done
clear
D)
5 units done
clear
View Solution play_arrow
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question_answer27)
A vector \[{{\overrightarrow{F}}_{1}}\]is along the positive X-axis. If its vector product with another vector \[{{\overrightarrow{F}}_{2}}\]is zero then \[{{\overrightarrow{F}}_{2}}\] could be [MP PMT 1987]
A)
\[4\hat{j}\] done
clear
B)
\[-(\hat{i}+\hat{j})\] done
clear
C)
\[(\hat{j}+\hat{k})\] done
clear
D)
\[(-4\hat{i})\] done
clear
View Solution play_arrow
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question_answer28)
If for two vectors \[\overrightarrow{A}\] and \[\overrightarrow{B},\overrightarrow{A}\times \overrightarrow{B}=0,\]the vectors
A)
Are perpendicular to each other done
clear
B)
Are parallel to each other done
clear
C)
Act at an angle of 60° done
clear
D)
Act at an angle of 30° done
clear
View Solution play_arrow
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question_answer29)
The angle between vectors \[(\overrightarrow{\text{A}}\times \overrightarrow{\text{B}})\] and \[(\overrightarrow{\text{B}}\times \overrightarrow{\text{A}})\] is
A)
Zero done
clear
B)
p done
clear
C)
\[\pi /4\] done
clear
D)
\[\pi /2\] done
clear
View Solution play_arrow
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question_answer30)
What is the angle between \[(\overrightarrow{P}+\overrightarrow{Q})\] and \[(\overrightarrow{P}\times \overrightarrow{Q})\]
A)
0 done
clear
B)
\[\frac{\pi }{2}\] done
clear
C)
\[\frac{\pi }{4}\] done
clear
D)
\[\pi \] done
clear
View Solution play_arrow
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question_answer31)
The resultant of the two vectors having magnitude 2 and 3 is 1. What is their cross product
A)
6 done
clear
B)
3 done
clear
C)
1 done
clear
D)
0 done
clear
View Solution play_arrow
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question_answer32)
Let \[\overrightarrow{A}=\hat{i}A\,\cos \theta +\hat{j}A\,\sin \theta \] be any vector. Another vector \[\overrightarrow{B}\] which is normal to A is [BHU 1997]
A)
\[\hat{i}\,B\,\cos \theta +j\,B\sin \theta \] done
clear
B)
\[\hat{i}\,B\,\sin \theta +j\,B\cos \theta \] done
clear
C)
\[\hat{i}\,B\,\sin \theta -j\,B\cos \theta \] done
clear
D)
\[\hat{i}\,B\,\cos \theta -j\,B\sin \theta \] done
clear
View Solution play_arrow
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question_answer33)
The angle between two vectors given by \[6\bar{i}+6\bar{j}-3\bar{k}\] and \[7\overline{i}+4\overline{j}+4\overline{k}\] is [EAMCET (Engg.) 1999]
A)
\[{{\cos }^{-1}}\left( \frac{1}{\sqrt{3}} \right)\] done
clear
B)
\[{{\cos }^{-1}}\left( \frac{5}{\sqrt{3}} \right)\] done
clear
C)
\[{{\sin }^{-1}}\left( \frac{2}{\sqrt{3}} \right)\] done
clear
D)
\[{{\sin }^{-1}}\left( \frac{\sqrt{5}}{3} \right)\] done
clear
View Solution play_arrow
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question_answer34)
A vector \[\overrightarrow{A}\] points vertically upward and \[\overrightarrow{B}\]points towards north. The vector product \[\overrightarrow{A}\times \overrightarrow{B}\] is [UPSEAT 2000]
A)
Zero done
clear
B)
Along west done
clear
C)
Along east done
clear
D)
Vertically downward done
clear
View Solution play_arrow
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question_answer35)
. Angle between the vectors \[(\hat{i}+\hat{j})\] and \[(\hat{j}-\hat{k})\] is
A)
90° done
clear
B)
0° done
clear
C)
180° done
clear
D)
60° done
clear
View Solution play_arrow
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question_answer36)
The position vectors of points A, B, C and D are \[A=3\hat{i}+4\hat{j}+5\hat{k},\,\,B=4\hat{i}+5\hat{j}+6\hat{k},\,\,C=7\hat{i}+9\hat{j}+3\hat{k}\] and \[D=4\hat{i}+6\hat{j}\] then the displacement vectors AB and CD are
A)
Perpendicular done
clear
B)
Parallel done
clear
C)
Antiparallel done
clear
D)
Inclined at an angle of \[\text{6}0{}^\circ \] done
clear
View Solution play_arrow
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question_answer37)
If force \[(\overrightarrow{F})=4\hat{i}+5\hat{j}\]and displacement \[(\overrightarrow{s})=3\hat{i}+6\hat{k}\] then the work done is [Manipal 1995]
A)
\[4\times 3\] done
clear
B)
\[5\times 6\] done
clear
C)
\[6\times 3\] done
clear
D)
\[4\times 6\] done
clear
View Solution play_arrow
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question_answer38)
If \[|\overrightarrow{A}\times \overrightarrow{B}|\,=\,|\overrightarrow{A}\,.\,\overrightarrow{B}|,\] then angle between \[\overrightarrow{A}\]and \[\overrightarrow{B}\] will be [AIIMS 2000; Manipal 2000]
A)
\[\text{3}0{}^\circ \] done
clear
B)
\[\text{45}{}^\circ \] done
clear
C)
\[\text{6}0{}^\circ \] done
clear
D)
\[\text{9}0{}^\circ \] done
clear
View Solution play_arrow
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question_answer39)
In an clockwise system [CPMT 1990]
A)
\[\hat{j}\times \hat{k}=\hat{i}\] done
clear
B)
\[\hat{i}.\,\hat{i}=0\] done
clear
C)
\[\hat{j}\times \hat{j}=1\] done
clear
D)
\[\hat{}\,.\,\hat{j}=1\] done
clear
View Solution play_arrow
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question_answer40)
The linear velocity of a rotating body is given by \[\overrightarrow{v}=\overrightarrow{\omega }\times \overrightarrow{r},\]where \[\overrightarrow{\omega }\] is the angular velocity and \[\overrightarrow{r}\] is the radius vector. The angular velocity of a body is \[\overrightarrow{\omega }=\hat{i}-2\hat{j}+2\hat{k}\] and the radius vector \[\overrightarrow{r}=4\hat{j}-3\hat{k},\] then \[|\overrightarrow{v}|\] is
A)
\[\sqrt{29}\]units done
clear
B)
\[\sqrt{31}\]units done
clear
C)
\[\sqrt{37}\]units done
clear
D)
\[\sqrt{41}\]units done
clear
View Solution play_arrow
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question_answer41)
Three vectors \[\overrightarrow{a},\,\overrightarrow{b}\]and \[\overrightarrow{c}\] satisfy the relation \[\overrightarrow{a}\,.\,\overrightarrow{b}=0\] and \[\overrightarrow{a}\,.\,\overrightarrow{c}=0.\] The vector \[\overrightarrow{a}\] is parallel to [AIIMS 1996]
A)
\[\overrightarrow{b}\] done
clear
B)
\[\overrightarrow{c}\] done
clear
C)
\[\overrightarrow{b}\,.\,\overrightarrow{c}\] done
clear
D)
\[\overrightarrow{b}\times \overrightarrow{c}\] done
clear
View Solution play_arrow
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question_answer42)
The diagonals of a parallelogram are \[2\,\hat{i}\] and \[2\hat{j}.\]What is the area of the parallelogram
A)
0.5 units done
clear
B)
1 unit done
clear
C)
2 units done
clear
D)
4 units done
clear
View Solution play_arrow
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question_answer43)
What is the unit vector perpendicular to the following vectors \[2\hat{i}+2\hat{j}-\hat{k}\] and \[6\hat{i}-3\hat{j}+2\hat{k}\]
A)
\[\frac{\hat{i}+10\hat{j}-18\hat{k}}{5\sqrt{17}}\] done
clear
B)
\[\frac{\hat{i}-10\hat{j}+18\hat{k}}{5\sqrt{17}}\] done
clear
C)
\[\frac{\hat{i}-10\hat{j}-18\hat{k}}{5\sqrt{17}}\] done
clear
D)
\[\frac{\hat{i}+10\hat{j}+18\hat{k}}{5\sqrt{17}}\] done
clear
View Solution play_arrow
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question_answer44)
The area of the parallelogram whose sides are represented by the vectors \[\hat{j}+3\hat{k}\] and \[\hat{i}+2\hat{j}-\hat{k}\] is
A)
\[\sqrt{61}\]sq. unit done
clear
B)
\[\sqrt{59}\]sq. unit done
clear
C)
\[\sqrt{49}\]sq. unit done
clear
D)
\[\sqrt{52}\]sq. unit done
clear
View Solution play_arrow
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question_answer45)
The position of a particle is given by \[\overrightarrow{r}=(\overrightarrow{i}+2\overrightarrow{j}-\overrightarrow{k})\] momentum \[\overrightarrow{P}=(3\overrightarrow{i}+4\overrightarrow{j}-2\overrightarrow{k}).\]The angular momentum is perpendicular to [EAMCET (Engg.) 1998]
A)
x-axis done
clear
B)
y-axis done
clear
C)
z-axis done
clear
D)
Line at equal angles to all the three axes done
clear
View Solution play_arrow
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question_answer46)
Two vector A and B have equal magnitudes. Then the vector A + B is perpendicular to
A)
\[A\times B\] done
clear
B)
A ? B done
clear
C)
3A ? 3B done
clear
D)
All of these done
clear
View Solution play_arrow
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question_answer47)
Find the torque of a force \[\overrightarrow{F}=-3\hat{i}+\hat{j}+5\hat{k}\] acting at the point \[\overrightarrow{r}=7\hat{i}+3\hat{j}+\hat{k}\] [CPMT 1997; CBSE PMT 1997; CET 1998; DPMT 2004]
A)
\[14\hat{i}-38\hat{j}+16\hat{k}\] done
clear
B)
\[4\hat{i}+4\hat{j}+6\hat{k}\] done
clear
C)
\[21\hat{i}+4\hat{j}+4\hat{k}\] done
clear
D)
\[-14\hat{i}+34\hat{j}-16\hat{k}\] done
clear
View Solution play_arrow
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question_answer48)
The value of \[(\overrightarrow{A}+\overrightarrow{B})\,\times (\overrightarrow{A}-\overrightarrow{B})\] is [RPET 1991, 2002; BHU 2002]
A)
0 done
clear
B)
\[{{A}^{2}}-{{B}^{2}}\] done
clear
C)
\[\overrightarrow{B}\times \overrightarrow{A}\] done
clear
D)
\[2(\overrightarrow{B}\times \overrightarrow{A})\] done
clear
View Solution play_arrow
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question_answer49)
If \[\vec{A}\] and \[\vec{B}\] are perpendicular vectors and vector \[\vec{A}=5\hat{i}+7\hat{j}-3\hat{k}\] and \[\vec{B}=2\hat{i}+2\hat{j}-a\hat{k}.\] The value of a is [EAMCET 1991]
A)
? 2 done
clear
B)
8 done
clear
C)
? 7 done
clear
D)
? 8 done
clear
View Solution play_arrow
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question_answer50)
A force vector applied on a mass is represented as \[\vec{F}=6\hat{i}-8\hat{j}+10\hat{k}\] and accelerates with \[1\ m/{{s}^{2}}\]. What will be the mass of the body in kg. [CMEET 1995]
A)
\[10\sqrt{2}\] done
clear
B)
\[20\] done
clear
C)
\[2\sqrt{10}\] done
clear
D)
10 done
clear
View Solution play_arrow
-
question_answer51)
Two adjacent sides of a parallelogram are represented by the two vectors \[\hat{i}+2\hat{j}+3\hat{k}\] and \[3\hat{i}-2\hat{j}+\hat{k}\]. What is the area of parallelogram [AMU 1997]
A)
8 done
clear
B)
\[8\sqrt{3}\] done
clear
C)
\[3\sqrt{8}\] done
clear
D)
192 done
clear
View Solution play_arrow
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question_answer52)
The position vectors of radius are \[2\hat{i}+\hat{j}+\hat{k}\] and \[2\hat{i}-3\hat{j}+\hat{k}\] while those of linear momentum are \[2\hat{i}+3\hat{j}-\hat{k}.\] Then the angular momentum is [BHU 1997]
A)
\[2\hat{i}-4\hat{k}\] done
clear
B)
\[4\hat{i}-8\hat{k}\] done
clear
C)
\[2\hat{i}-4\hat{j}+2\hat{k}\] done
clear
D)
\[4\hat{i}-8\hat{k}\] done
clear
View Solution play_arrow
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question_answer53)
What is the value of linear velocity, if \[\vec{\omega }=3\hat{i}-4\hat{j}+\hat{k}\] and \[\vec{r}=5\hat{i}-6\hat{j}+6\hat{k}\] [CBSE PMT 1999; CPMT 1999, 2001; Pb. PMT 2000; Pb. CET 2000]
A)
\[6\hat{i}-2\hat{j}+3\hat{k}\] done
clear
B)
\[6\hat{i}-2\hat{j}+8\hat{k}\] done
clear
C)
\[4\hat{i}-13\hat{j}+6\hat{k}\] done
clear
D)
\[-18\hat{i}-13\hat{j}+2\hat{k}\] done
clear
View Solution play_arrow
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question_answer54)
Dot product of two mutual perpendicular vector is [Haryana CEET 2002]
A)
0 done
clear
B)
1 done
clear
C)
¥ done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer55)
When \[\vec{A}.\vec{B}=-|A||B|,\] then [Orissa JEE 2003]
A)
\[\vec{A}\] and \[\vec{B}\] are perpendicular to each other done
clear
B)
\[\vec{A}\] and \[\vec{B}\] act in the same direction done
clear
C)
\[\vec{A}\] and \[\vec{B}\] act in the opposite direction done
clear
D)
\[\vec{A}\] and \[\vec{B}\] can act in any direction done
clear
View Solution play_arrow
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question_answer56)
If \[|\vec{A}\times \vec{B}|=\sqrt{3}\vec{A}.\vec{B},\] then the value of\[|\vec{A}+\vec{B}|\] is [CBSE PMT 2004]
A)
\[{{\left( {{A}^{2}}+{{B}^{2}}+\frac{AB}{\sqrt{3}} \right)}^{1/2}}\] done
clear
B)
\[A+B\] done
clear
C)
\[{{({{A}^{2}}+{{B}^{2}}+\sqrt{3}AB)}^{1/2}}\] done
clear
D)
\[{{({{A}^{2}}+{{B}^{2}}+AB)}^{1/2}}\] done
clear
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-
question_answer57)
A force \[\vec{F}=3\hat{i}+c\hat{j}+2\hat{k}\] acting on a particle causes a displacement \[\vec{S}=-4\hat{i}+2\hat{j}-3\hat{k}\] in its own direction. If the work done is 6J, then the value of c will be [DPMT 1997]
A)
12 done
clear
B)
6 done
clear
C)
1 done
clear
D)
0 done
clear
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question_answer58)
A force \[\vec{F}=(5\hat{i}+3\hat{j})\ N\]is applied over a particle which displaces it from its original position to the point \[\vec{s}=(2\hat{i}-1\hat{j})\]m. The work done on the particle is [BHU 2001]
A)
+ 11 J done
clear
B)
+ 7 J done
clear
C)
+ 13 J done
clear
D)
? 7 J done
clear
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-
question_answer59)
If a vector \[\vec{A}\] is parallel to another vector \[\vec{B}\] then the resultant of the vector \[\vec{A}\times \vec{B}\] will be equal to [Pb. CET 1996]
A)
A done
clear
B)
\[\vec{A}\] done
clear
C)
Zero vector done
clear
D)
Zero done
clear
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