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JEE Main & Advanced Mathematics Vector Algebra Question Bank Self Evaluation Test - Vector Algebra

  • question_answer
    If \[(\vec{a}\times \vec{b})\times \vec{c}=\vec{a}\times (\vec{b}\times \vec{c})\] where \[\vec{a},\vec{b}\] and \[\vec{c}\] are any three vectors such that \[\vec{a}.\vec{b}\ne 0,\vec{b}.\vec{c}\ne 0\] then \[\vec{a}\] and \[\vec{c}\] are  

    A) Inclined at an angle of \[\frac{\pi }{3}\] between them

    B) Inclined at an angle of \[\frac{\pi }{6}\] between them

    C) Perpendicular

    D) Parallel

    Correct Answer: D

    Solution :

    [d] \[(\vec{a}\times \vec{b})\times \vec{c}=\vec{a}\times (\vec{b}\times \vec{c}),\vec{a}.\vec{b}\ne 0,\vec{b}.\vec{c}\ne 0\] \[\Rightarrow (\vec{a}.\vec{c}).\vec{b}-(\vec{b}.\vec{c})\vec{a}=(\vec{a}.\vec{c}).\vec{b}-(\vec{a}.\vec{b}).\vec{c}\] \[\Rightarrow (\vec{a}.\vec{b}).\vec{c}=(\vec{b}.\vec{c})\vec{a}\Rightarrow \vec{a}\parallel \vec{c}.\]


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