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KVPY Sample Paper KVPY Stream-SX Model Paper-8

  • question_answer
    If \[\vec{a}\] and \[\vec{b}\] are two vectors such that \[\left| \vec{a}+\vec{b} \right|=2\] then value of \[\left[ \vec{a}\,\,\vec{b}\,\,\vec{a}\times \vec{b} \right]\] is equal to -

    A) 1                                 

    B) 2    

    C) 4                     

    D) 0

    Correct Answer: C

    Solution :

    \[|\,\vec{a}\,\,\times \,\,\vec{b}\,|\,=2\]
    \[[\vec{a}\,\,\vec{b}\,\,\vec{a}\,\,\times \,\,\vec{b}]\]
    \[[\vec{a}\,\,\times \,\,\vec{b}\,\,\,\vec{a}\,\,\vec{b}]=(\vec{a}\,\,\times \,\,\vec{b}).{{(\vec{a}\,\,\times \,\,\vec{b})}^{2}}=|\vec{a}\,\,\times \,\,\vec{b}|\]        


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