JEE Main & Advanced Physics Vectors Question Bank

done Topic Test - Vectors Total Questions - 35

• question_answer1)
  The component of \[(\hat{i}+\hat{j})\] along \[(\hat{i}-\hat{j})\] is
  A)
  0 done clear
  B)
  \[\frac{1}{\sqrt{2}}(\hat{i}-\hat{j})\] done clear
  C)
  \[\frac{1}{\sqrt{2}}(\hat{i}+\hat{j})\] done clear
  D)
  \[\frac{\hat{i}-\hat{j}}{2}\] done clear
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• question_answer2)
  A particle is moving with velocity 5 m/s towards east and its velocity changes to 5 m/s north in 10 seconds. Find the average acceleration in 10 seconds.
  A)
  \[\sqrt{2}N-W\] done clear
  B)
  \[\frac{1}{\sqrt{2}}N-W\] done clear
  C)
  \[\frac{1}{\sqrt{2}}N-E\] done clear
  D)
  \[\sqrt{2}N-E\] done clear
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• question_answer3)
  The vector \[\vec{P}=a\hat{i}+a\hat{j}+3\hat{k}\] and \[\vec{Q}=a\hat{i}-2\hat{j}-\hat{k}\] are perpendicular to each other. The positive value of a is
  A)
  3 done clear
  B)
  4 done clear
  C)
  9 done clear
  D)
  13 done clear
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• question_answer4)
  A particle moves along a path ABCD as shown in the figure. Then the magnitude of net displacement of the particle from position A to D is:
  A)
  10 m done clear
  B)
  \[5\sqrt{2}\,m\] done clear
  C)
  9 m done clear
  D)
  \[7\sqrt{2}\,m\] done clear
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• question_answer5)
  A body goes 10 km north and 20 km east. What will be the displacement from initial point?
  A)
  22.36 km done clear
  B)
  2 km done clear
  C)
  5 km done clear
  D)
  30 km done clear
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• question_answer6)
  The three vectors \[\vec{A}=3\hat{i}-2\hat{j}-\hat{k},\]\[\vec{B}=\hat{i}-3\hat{j}+5\hat{k}\] and \[\vec{C}=2\hat{i}-\hat{j}-4\hat{k}\] does not form
  A)
  an equilateral triangle done clear
  B)
  isosceles triangle done clear
  C)
  a right angled triangle done clear
  D)
  no triangle done clear
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• question_answer7)
  Find the torque of a force \[\vec{F}=-3\hat{i}+\hat{j}+5\hat{k}\] acting at a point \[\vec{r}=7\hat{i}+3\hat{j}+\hat{k}\]
  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
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• question_answer8)
  Two forces \[{{\vec{F}}_{1}}=10\hat{i}-\hat{j}-15\hat{k}\] and \[{{\vec{F}}_{2}}=10\hat{i}-\hat{j}-15\hat{k}\] act on a single point. The angle between \[{{\vec{F}}_{1}}\] and \[{{\vec{F}}_{2}}\] is nearly
  A)
  \[{{30}^{o}}\] done clear
  B)
  \[{{45}^{o}}\] done clear
  C)
  \[{{60}^{o}}\] done clear
  D)
  \[{{90}^{o}}\] done clear
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• question_answer9)
  It is found that \[|A+B|\,=\,|A|\]. This necessarily  implies.
  A)
  \[B=0\] done clear
  B)
  \[\vec{A},\vec{B}\] antiparallel done clear
  C)
  \[\vec{A},\vec{B}\] are perpendicular done clear
  D)
  \[\vec{A}.\vec{B}\le 0\] done clear
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• question_answer10)
  The angle between two vector \[\overrightarrow{A}\And \overrightarrow{B}\] is \[\theta \]. vector \[\overrightarrow{R}\] is the resultant of vectors \[\overrightarrow{A}\And \overrightarrow{B},\] if \[\overrightarrow{R}\] makes an angle \[\frac{\theta }{2}\] with \[\overrightarrow{A}\] then
  A)
  A = 2B done clear
  B)
  A = B/2 done clear
  C)
  A = B done clear
  D)
  AB = 1 done clear
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• question_answer11)
  The unit vector parallel to the resultant of the vectors \[\overrightarrow{A}=4\hat{i}+3j+6\hat{k}\] and \[\overrightarrow{B}=-\hat{i}+3j-8\hat{k}\] is
  A)
  \[\frac{1}{7}(3\hat{i}+6j-2\hat{k})\] done clear
  B)
  \[\frac{1}{7}(3\hat{i}+6j+2\hat{k})\] done clear
  C)
  \[\frac{1}{49}(3\hat{i}+6j-2\hat{k})\] done clear
  D)
  \[\frac{1}{49}(3\hat{i}-6j+2\hat{k})\] done clear
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• question_answer12)
  The resultant of \[\vec{A}\] and \[\vec{B}\] is \[{{\vec{R}}_{1}}\]. On reversing the vector \[\vec{B},\] the resultant becomes \[{{\vec{R}}_{2}}\]. What is the value of \[R_{1}^{2}\,+\,R_{2}^{2}\,?\]
  A)
  \[{{A}^{2}}+\,{{B}^{2}}\] done clear
  B)
  \[{{A}^{2}}-{{B}^{2}}\]        done clear
  C)
  \[2({{A}^{2}}+\,{{B}^{2}})\] done clear
  D)
  \[2({{A}^{2}}-\,{{B}^{2}})\] done clear
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• question_answer13)
  At what angle should the two forces 2P and \[\sqrt{2}\,P\] act so that the resultant force is \[P\sqrt{10}\,?\]
  A)
  \[45{}^\circ \]   done clear
  B)
  \[{{60}^{o}}\] done clear
  C)
  \[{{90}^{o}}\] done clear
  D)
  \[{{120}^{o}}\] done clear
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• question_answer14)
  What is correct?
  A)
  \[|\vec{a}-\vec{b}|\,=|\vec{a}|-|\vec{b}|\] done clear
  B)
  \[|\vec{a}-\vec{b}|\,\le |\vec{a}|-|\vec{b}|\] done clear
  C)
   \[|\vec{a}-\vec{b}|\,\ge |\vec{a}|-|\vec{b}|\] done clear
  D)
  \[|\vec{a}-\vec{b}|\,<|\vec{a}|-|\vec{b}|\] done clear
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• question_answer15)
  P, Q and R are three coplanar forces acting at a point and are in equilibrium. Given \[P=1.9318\,kg\,wt,\] \[sin{{\theta }_{1}}=0.9659,\] the value of R is (in kg wt) 
  A)
  0.9659 done clear
  B)
  2 done clear
  C)
  1 done clear
  D)
  \[\frac{1}{2}\] done clear
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• question_answer16)
  The vectors from origin to the points A and B are \[\vec{A}=3\hat{i}\,-6\hat{j}\,+2\hat{k}\] and \[\vec{B}=2\hat{i}+\,\hat{j}\,-2\hat{k}\] respectively. The area of the triangle OAB be
  A)
  \[\frac{5}{2}\,\sqrt{17}\,sq\,units\] done clear
  B)
  \[\frac{2}{5}\,\sqrt{17}\,sq\,unit\] done clear
  C)
  \[\frac{3}{5}\,\sqrt{17}\,sq\,unit\]            done clear
  D)
  \[\frac{5}{3}\,\sqrt{17}\,sq\,unit\] done clear
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• question_answer17)
  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 \[\lambda \] is
  A)
  0 done clear
  B)
  2 done clear
  C)
  3 done clear
  D)
  4 done clear
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• question_answer18)
  If a unit vector is represented by \[0.5\hat{i}\,+0.8\hat{j}\,+\,c\hat{k},\] then the value of c is
  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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• question_answer19)
  Obtain the directions of vector \[(\vec{A}\,-\vec{B}),\] if \[\vec{A}=2\hat{i}+3\hat{j}=\,\hat{k},\vec{B}\,=2\hat{i}+2\hat{j}+3\hat{k}\]
  A)
  \[0,\,\frac{1}{\sqrt{5}}\,,\,\frac{-2}{\sqrt{5}}\] done clear
  B)
  \[0,\,\frac{1}{\sqrt{5}}\,,\,\frac{1}{\sqrt{5}}\] done clear
  C)
  0, 0, \[\frac{1}{\sqrt{5}}\] done clear
  D)
  None of these done clear
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• question_answer20)
  A vector having magnitude 30 unit makes equal angles with each of X, Y and Z axes. The components of vector along each of X, Y and Z axes are
  A)
  \[10\sqrt{3}\] unit done clear
  B)
  \[\frac{10}{\sqrt{3}}\] unit done clear
  C)
  \[15\sqrt{3}\] unit done clear
  D)
  10 unit done clear
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• question_answer21)
  Unit vector perpendicular to vector \[\vec{A}\,=3\hat{i}+\,\hat{j}\] and \[\vec{B}\,=2\hat{i}-\,\hat{j}-5\hat{k}\] both is
  A)
  \[\pm \,\frac{3j-2\hat{k}}{\sqrt{11}}\] done clear
  B)
  \[\pm \,\frac{(\hat{i}-3\hat{j}+\,\hat{k})}{\sqrt{11}}\] done clear
  C)
  \[\pm \,\frac{-\hat{j}+2\,\hat{k}}{\sqrt{13}}\] done clear
  D)
  \[\pm \,\frac{\hat{i}+3\hat{j}-\,\hat{k}}{\sqrt{13}}\] done clear
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• question_answer22)
  The value of  \[\hat{i}\,\times \,(\hat{i}\times \,\vec{a})\,+\hat{j}\,\times \,(\hat{j}+\vec{a})\,+\hat{k}+(\,\hat{k}\times \hat{a})\] is
  A)
  \[\vec{a}\] done clear
  B)
  \[\vec{a}\,\times \,\hat{k}\] done clear
  C)
  \[-2\vec{a}\]      done clear
  D)
  \[-\,\vec{a}\] done clear
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• question_answer23)
  If  \[\vec{a}\times \vec{b}\,+\vec{c}=0,\] then \[\vec{a}\times \vec{b}\,\] is
  A)
  \[\vec{a}\times \vec{b}\] done clear
  B)
  \[\vec{c}\times \vec{b}\,\] done clear
  C)
  \[\vec{a}\times \vec{c}\] done clear
  D)
  None of these done clear
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• question_answer24)
  The sum of the magnitudes of two forces acting at point is 18 and the magnitude of their resultant is 12. If the resultant is at \[90{}^\circ \] with the force of smaller magnitude, what are the magnitudes of forces?
  A)
  12, 5 done clear
  B)
  14, 4 done clear
  C)
  5, 13 done clear
  D)
  10, 8 done clear
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• question_answer25)
  Given that X \[\vec{A}\,+\vec{B}+\vec{C}\]= 0, out of three vectors two are equal in magnitude and the magnitude of third vector is \[\sqrt{2}\] times that of either of two having equal magnitude. Then, angle between vectors are given by
  A)
  \[30{}^\circ ,\text{ }60{}^\circ ,\text{ }90{}^\circ \] done clear
  B)
  \[45{}^\circ ,\text{ }45{}^\circ ,\text{ }90{}^\circ \] done clear
  C)
  \[90{}^\circ ,\text{ }135{}^\circ ,\text{ }45{}^\circ \] done clear
  D)
  \[90{}^\circ ,\text{ }135{}^\circ ,\text{ }135{}^\circ \] done clear
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• question_answer26)
  Given \[\vec{A}\,=\hat{i}+\hat{j}\,+\hat{k}\] and \[\vec{B}\,=-\hat{i}-\hat{j}-\hat{k},\,(\vec{A}-\vec{B})\] will make angle with \[\vec{A}\] as
  A)
  \[0{}^\circ \] done clear
  B)
  \[{{180}^{o}}\]           done clear
  C)
  \[90{}^\circ \] done clear
  D)
  \[60{}^\circ \] done clear
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• question_answer27)
  Find a vector of magnitude 5 along BA where coordinates of points A and B are (0, 1, 3) and   (1, 4, 6) respectively
  A)
  \[\left( \frac{5}{\sqrt{19}} \right)[\hat{i}+3\hat{j}+3\hat{k}]\] done clear
  B)
  \[-\left( \frac{5}{\sqrt{19}} \right)[\hat{i}+3\hat{j}+3\hat{k}]\] done clear
  C)
  \[5[\hat{i}+3\hat{j}+3\hat{k}]\] done clear
  D)
  \[-5[\hat{i}+3\hat{j}+3\hat{k}]\] done clear
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• question_answer28)
  \[\vec{A}-\vec{B}\] and \[\vec{A}\] are parallel. If \[|\vec{A}\times \vec{B}|\,=\,|\vec{A}.\vec{B}|,\] then angle between \[\vec{A}\] and \[\vec{B}\] will be
  A)
  \[30{}^\circ \] done clear
  B)
  \[45{}^\circ \] done clear
  C)
  \[60{}^\circ \] done clear
  D)
  \[90{}^\circ \] done clear
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• question_answer29)
  A metal sphere is hung by a string fixed to a wall. The sphere is pushed away from the wall by a stick. The forces acting on the sphere are shown in the second diagram. Which of the following statements is wrong?             
  A)
  \[P=W\tan \theta \] done clear
  B)
  \[\vec{T}+\vec{P}+\vec{W}=0\] done clear
  C)
  \[{{T}^{2}}={{P}^{2}}+{{W}^{2}}\] done clear
  D)
  \[T=P+W\] done clear
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• question_answer30)
  Component of the vector \[\vec{A}=\,2\hat{i}+3\hat{j}\] along the vector \[\vec{B}\,=(\hat{i}+\,\hat{j})\,\] is
  A)
  \[\frac{5}{\sqrt{2}}\]      done clear
  B)
  \[4\sqrt{2}\] done clear
  C)
  \[\frac{\sqrt{2}}{3}\]      done clear
  D)
  None of these done clear
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• question_answer31)
  Which of the following is a unit vector?
  A)
  \[\hat{i}+\,\hat{j}\]        done clear
  B)
  \[\cos \,\theta \hat{i}-\sin \,\theta \hat{j}\] done clear
  C)
  \[\sin \,\theta \hat{i}+2\,x\cos \theta \hat{j}\] done clear
  D)
  \[\frac{1}{\sqrt{3}}\,(\hat{i}+\,\hat{j})\] done clear
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• question_answer32)
  A vector \[\vec{a}\] is turned without a change in its length through a small angle \[d\theta \]. The value of \[|\Delta \vec{a}|\] and \[\Delta a\] are respectively
  A)
  \[0,\,a\,d\theta \] done clear
  B)
  \[a,\,d\theta ,\,\,0\] done clear
  C)
  0, 0 done clear
  D)
  None of these done clear
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• question_answer33)
  If three vectors along coordinate axes represent the adjacent sides of a cube of length b, then the unit vector along its diagonal passing through the origin will be
  A)
  \[\frac{\hat{i}\,+\,\hat{j}\,+\,\hat{k}}{\sqrt{2}}\] done clear
  B)
  \[\frac{\hat{i}\,+\,\hat{j}\,+\,\hat{k}}{\sqrt{3b}}\] done clear
  C)
  \[\hat{i}\,+\,\hat{j}\,+\,\hat{k}\] done clear
  D)
  \[\frac{\hat{i}\,+\,\hat{j}\,+\,\hat{k}}{\sqrt{3}}\] done clear
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• question_answer34)
  If \[{{\bar{a}}_{1}}\] and \[{{\bar{a}}_{2}}\] are two non-collinear unit vectors and \[|{{\bar{a}}_{1}}+{{\bar{a}}_{2}}|=\sqrt{3},\] then the value of \[({{\bar{a}}_{1}}-{{\bar{a}}_{2}}).(2{{\bar{a}}_{1}}+{{\bar{a}}_{2}})\] is
  A)
  2 done clear
  B)
  3/2 done clear
  C)
  ½ done clear
  D)
  1 done clear
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• question_answer35)
  If \[\vec{A}\times \vec{B}=(\vec{C}+\vec{D}),\] then select the correct alternative
  A)
  \[\vec{B}\] is parallel to \[\vec{C}+\vec{D}\] done clear
  B)
  \[\vec{A}\] is perpendicular to \[\vec{C}\] done clear
  C)
  component of \[\vec{C}\] along \[\vec{A}=\] component of \[\vec{D}\] along \[\vec{A}\] done clear
  D)
  component of \[\vec{C}\] along \[\vec{A}=-\] component of\[\vec{D}\] along \[\vec{A}\] done clear
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