JEE Main & Advanced Physics Vectors Question Bank

done Multiplication of Vectors Total Questions - 59

• 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

• 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

• 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

• 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

• 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

• 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

• 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

• 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

• 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

• 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

• 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

• 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

• 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

• 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

• 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

• 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

• 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

• 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

• 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

• 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

• 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

• 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

• 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

• 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

• 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

• 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

• 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

• 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

• 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

• 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

• 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

• 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

• 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

• 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

• 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

• 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

• 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

• 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

• 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

• 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

• 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

• 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

• 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

• 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

• 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

• 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

• 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

• 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

• 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

• 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
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• 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
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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
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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
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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
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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
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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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