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JEE Main & Advanced Mathematics Vector Algebra Question Bank Mock Test - Vector Algebra

  • question_answer
    Given three vectors \[\vec{a}=6\hat{i}-3\hat{j},\hat{b}=2\hat{i}-6\hat{j}\] and \[\vec{c}=-2\hat{i}+21\hat{j}\] such that \[\overrightarrow{\alpha }=\vec{a}+\vec{b}+\vec{c}\]. Then the resolution of the vector \[\overrightarrow{\alpha }\] into components with respect to \[\vec{a}\] and \[\vec{b}\] is given by

    A) \[3\vec{a}-2\vec{b}\]

    B) \[3\vec{b}\]\[-\]\[2\vec{a}\]

    C) \[2\vec{a}-3\vec{b}\]

    D) \[\vec{a}-2\vec{b}\]

    Correct Answer: C

    Solution :

    [c] \[\vec{\alpha }=\vec{a}+\vec{b}+\vec{c}=6\hat{i}+12\hat{j}\] Let \[\vec{\alpha }=x\vec{a}+y\vec{b}\Rightarrow 6x+2y=6\] And \[-\,3x-6y=12\] \[\therefore x=2,y=-3\] \[\therefore \vec{\alpha }=2\vec{a}-3\vec{b}\]     


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