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JEE Main & Advanced Mathematics Vector Algebra Question Bank Vector triple product

  • question_answer
    If \[a=i+j+k,\,\,b=i+j,\,\,c=i\] and \[(a\times b)\times c=\lambda \,a+\mu \,b\], then \[\lambda +\mu =\] [EAMCET 2003]

    A)                0

    B)               1

    C)               2

    D)               3

    Correct Answer: A

    Solution :

               \[\mathbf{a}\,.\,\mathbf{c}=1\] and \[\mathbf{b}\,.\,\mathbf{c}=1\]                    Given that\[(\mathbf{a}\times \mathbf{b})\times \mathbf{c}=(\mathbf{c}\,.\,\mathbf{a})\mathbf{b}-(\mathbf{c}\,.\,\mathbf{b})\,\mathbf{a}=\mu \,\mathbf{b}+\lambda \mathbf{a}\]                    where \[\mu =\mathbf{c}\,.\,\mathbf{a}=1,\,\,\lambda =-\,(\mathbf{c}\,.\,\mathbf{b})=-\,1\]                    \[\Rightarrow \,\,\mu +\lambda =1-1=0\].


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