JEE Main & Advanced Physics Vectors Question Bank

done Fundamentals of Vectors Total Questions - 34

• question_answer1)
  The vector projection of a vector \[3\hat{i}+4\hat{k}\]on y-axis is                                                        [RPMT 2004]
  A)
             5     done clear
  B)
             4 done clear
  C)
             3     done clear
  D)
              Zero done clear
  View Solution play_arrow

• question_answer2)
  Position of a particle in a rectangular-co-ordinate 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
  View Solution play_arrow

• question_answer3)
  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
  View Solution play_arrow

• question_answer4)
  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
  View Solution play_arrow

• question_answer5)
  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
  View Solution play_arrow

• question_answer6)
  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
  View Solution play_arrow

• question_answer7)
  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
  View Solution play_arrow

• question_answer8)
  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 y­­-axis 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
  View Solution play_arrow

• question_answer9)
  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
  View Solution play_arrow

• question_answer10)
  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
  View Solution play_arrow

• question_answer11)
  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
  View Solution play_arrow

• question_answer12)
  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
  View Solution play_arrow

• question_answer13)
  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
  View Solution play_arrow

• question_answer14)
  Given vector \[\overrightarrow{A}=2\hat{i}+3\hat{j},\]the angle between \[\overrightarrow{A}\]and y-axis 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
  View Solution play_arrow

• question_answer15)
  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
  View Solution play_arrow

• question_answer16)
  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
  View Solution play_arrow

• question_answer17)
  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
  View Solution play_arrow

• question_answer18)
  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
  View Solution play_arrow

• question_answer19)
  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
  View Solution play_arrow

• question_answer20)
  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
  View Solution play_arrow

• question_answer21)
  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
  View Solution play_arrow

• question_answer22)
  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
  View Solution play_arrow

• question_answer23)
  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
  View Solution play_arrow

• question_answer24)
  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
  View Solution play_arrow

• question_answer25)
  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
  View Solution play_arrow

• question_answer26)
  A boy walks uniformally along the sides of a rectangular park of size 400 m× 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
  View Solution play_arrow

• question_answer27)
  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
  View Solution play_arrow

• question_answer28)
  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
  View Solution play_arrow

• question_answer29)
  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 Z-axis 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
  View Solution play_arrow

• question_answer30)
  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
  View Solution play_arrow

• question_answer31)
  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
  View Solution play_arrow

• question_answer32)
  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
  View Solution play_arrow

• question_answer33)
  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
  View Solution play_arrow

• question_answer34)
  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
  View Solution play_arrow