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

  • question_answer
    If \[\mathbf{a}=3\mathbf{i}-2\mathbf{j}+2\mathbf{k},\,\,\,\mathbf{b}=6\mathbf{i}+4\mathbf{j}-2\mathbf{k}\] and \[\mathbf{c}=3\mathbf{i}-2\mathbf{j}-4\mathbf{k}\], then \[\mathbf{a}\,.\,\,(\mathbf{b}\times \mathbf{c})\] is [Karnataka CET 2001]

    A)             122

    B)             ? 144

    C)             120

    D)             ? 120

    Correct Answer: B

    Solution :

                    \[\mathbf{a}\,.\,(\mathbf{b}\times \mathbf{c})=\left| \,\begin{matrix}    3 & -2 & \,\,2  \\    6 & \,\,\,4 & -2  \\    3 & -2 & -4  \\ \end{matrix}\, \right|\]                 \[=3\,[-16-4]+2\,[-24+6]+2\,[-12-12]\]                 = ? 60 ? 36 ? 48 = ? 144.


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