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

  • question_answer
    The volume of the parallelopiped whose edges are represented by \[-12\mathbf{i}+\alpha \mathbf{k},\,\,3\mathbf{j}-\mathbf{k}\] and \[2\mathbf{i}+\mathbf{j}-15\mathbf{k}\] is 546. Then \[\alpha =\]            [IIT Screening 1989; MNR 1987]

    A)             3

    B)             2

    C)             ? 3

    D)             ­? 2

    Correct Answer: C

    Solution :

                    Since \[\left| \begin{matrix}    -12 & 0 & \alpha   \\    0 & 3 & -1  \\    2 & 1 & -15  \\ \end{matrix} \right|=546\Rightarrow \alpha =-3.\]


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