JEE Main & Advanced Mathematics Vector Algebra Question Bank

done Numerical Value Type Questions - Vector Total Questions - 15

• question_answer1)
  If \[\hat{i}-\hat{j}+2\hat{k},\,2\hat{i}+\hat{j}-\hat{k}\] and \[3\hat{i}-\hat{j}+2\,\,\hat{k}\] are position vectors of vertices of a triangle, if its area is \[\sqrt{k}\] then find k.
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• question_answer2)
  A particle acted on by constant forces \[4\,\hat{i}+\hat{j}-3\,\hat{k}\] and \[3\,\,\hat{i}+\hat{j}-\hat{k}\] is displaced from the point \[\hat{i}+2\hat{j}+3\hat{k}\] to the point \[5\,\hat{i}+4\hat{j}+\hat{k}.\] Then find the total work done by forces.
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• question_answer3)
  Let \[\vec{a}=2\,\hat{i}+\hat{j}-2\hat{k}\] and \[\vec{b}=\hat{i}+\hat{j}.\] If \[\overrightarrow{c}\] is a vector such that \[\vec{a}.\vec{c}=\left| {\vec{c}} \right|,\left| \vec{c}-\vec{a} \right|=2\sqrt{2}\] and the angle between \[\vec{a}\times \vec{b}\] and \[\overrightarrow{c}\] is \[30{}^\circ ,\] then find value of \[\left| \left( \vec{a}\times \vec{b} \right)\times \vec{c} \right|.\]
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• question_answer4)
  If \[|\overrightarrow{a}|=3,\,\,|\overrightarrow{b}|=4\] and \[|\overrightarrow{a}\,+\,\overrightarrow{b}|=5,\] then find \[|\overrightarrow{a}\,-\,\overrightarrow{b}|\].
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• question_answer5)
  ABCD is a quadrilateral with \[\overrightarrow{AB}=\overrightarrow{a},\,\,\overrightarrow{AD}=\vec{b}\] and \[\overrightarrow{AC}=2\overrightarrow{a}\,\,+3\,\,\vec{b}.\] If its area is \[\alpha \] times the area of the parallelogram gm with AB, AD as adjacent sides, then find the value of \[\alpha \].
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• question_answer6)
  Let \[\overrightarrow{OA}=\overrightarrow{a},\,\,\overrightarrow{OB}=10\,\overrightarrow{a}+2\,\vec{b}\] and \[\overrightarrow{OC}=\vec{b}\] where A and C are non-collinear points. Let p denote the area of the quadrilateral OABC, and let q denote the area of the parallelogram with OA and OC as adjacent sides. If \[p=kq,\] then find value of k.
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• question_answer7)
  If vectors \[\overrightarrow{AB}=-3\,\hat{i}+4\,\hat{k}\] and \[\overrightarrow{AC}=5\,\hat{i}-2\hat{j}+4\hat{k}\] are the sides of a \[\Delta ABC,\] if the length of the median through A is \[\sqrt{k}\] then find k.
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• question_answer8)
  If \[|\overrightarrow{a}|\,\,=\,\,|\vec{b}|=1\] and \[|\overrightarrow{a}\,+\,\overrightarrow{b}|=\sqrt{3,}\] then find the value of \[\left( 3\,\,\overrightarrow{a}-4\,\vec{b} \right).\left( 2\,\overrightarrow{a}+5\,\overrightarrow{b} \right).\]
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• question_answer9)
  Find the area of the parallelogram whose diagonals are \[\vec{a}-\vec{b}\] and \[3\,\vec{a}+\vec{b},\] where \[|\overrightarrow{a}|\,\,=2|\overrightarrow{b}|\,\,=2\] and the angle between \[\vec{a}\] and \[\vec{b}\] is \[\pi /6\].
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• question_answer10)
  Let \[\left| {\vec{a}} \right|=1,\,\left| {\vec{b}} \right|=2,\,\,\left| {\vec{c}} \right|=3\] and \[\vec{a}\bot \left( \vec{b}+\vec{c} \right),\]  \[\,\vec{b}\bot \left( \vec{c}+\vec{a} \right)\] and \[\vec{c}\bot (\vec{a}+\overrightarrow{b})\]. If the value of \[\left| \vec{a}+\vec{b}+\vec{c} \right|\] is \[\sqrt{k}\] then find k.
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• question_answer11)
  If vectors \[2\,\hat{i}-\hat{j}+\hat{k},\,\,\hat{i}+2\hat{j}-3\hat{k}\] and \[3\hat{i}+a\hat{j}+5\hat{k}\] are coplanar, then find value of 'a'.
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• question_answer12)
  If the vectors \[\vec{a}+\vec{b}-\lambda \vec{c},\,\,3\vec{a}-2\vec{b}\,\,+4\vec{c},\]\[\,3\vec{a}-7\vec{b}+14\vec{c}\] are linearly dependent (\[\vec{a},\,\,\vec{b},\,\,\vec{c}\] are non-zero non- coplanar) then find the value of\[\lambda \].
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• question_answer13)
  If \[\vec{u},\vec{v},\vec{w}\] are vectors such that \[\vec{u}+\vec{v}+\vec{w}=0,\]\[\left| {\vec{u}} \right|=3,\,\,\left| {\vec{v}} \right|=4\,\,\left| {\vec{w}} \right|=5,\] then find value of \[\vec{u}.\vec{v}+\vec{v}.\vec{w}+\vec{w}.\vec{u}.\]
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• question_answer14)
  Let \[\left| \,\,\vec{a}\,\, \right|=1\] and \[\left| \,\,\vec{b}\,\, \right|=3.\] If \[\vec{a}+\lambda \vec{b}\] and \[\vec{a}-\lambda \vec{b}\] are mutually perpendicular vectors, then find value of \[\left| \lambda  \right|.\]
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• question_answer15)
  Find the volume of parallelepiped whose coterminus edges are represented by \[\vec{a}=2\hat{i}-3\hat{j}+4\hat{k},\]\[\vec{b}=\hat{i}+2\hat{j}-\hat{k}\] and \[\vec{c}=3\hat{i}-\hat{j}+2\hat{k}.\]
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