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JEE Main & Advanced Mathematics Vector Algebra Question Bank Scalar triple product and their applications

  • question_answer
    If \[\mathbf{a}=2\mathbf{i}+\mathbf{j}-\mathbf{k},\,\,\mathbf{b}=\mathbf{i}+2\mathbf{j}+\mathbf{k}\] and \[\mathbf{c}=\mathbf{i}-\mathbf{j}+2\mathbf{k},\] then \[\mathbf{a}\,.\,(\mathbf{b}\times \mathbf{c})=\]                                    [RPET 1989, 2001]

    A)             6

    B)             10

    C)             12

    D)             24

    Correct Answer: C

    Solution :

                    \[\mathbf{a}\,.\,(\mathbf{b}\times \mathbf{c})=\mathbf{a}\,.\,\left| \,\begin{matrix}    \mathbf{i} & \mathbf{j} & \mathbf{k}  \\    1 & 2 & 1  \\    1 & -1 & 2  \\ \end{matrix}\, \right|=\mathbf{a}\,.\,(5\mathbf{i}-\mathbf{j}-3\mathbf{k})\]                                 \[=(2\mathbf{i}+\mathbf{j}-\mathbf{k})\,.\,(5\mathbf{i}-\mathbf{j}-3\mathbf{k})=10-1+3=12\].


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