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

  • question_answer
    If three vectors \[\mathbf{a}=12\mathbf{i}+4\mathbf{j}+3\mathbf{k},\,\,\]\[\mathbf{b}=8\mathbf{i}-12\mathbf{j}-9\mathbf{k}\] and \[\mathbf{c}=33\mathbf{i}-4\mathbf{j}-24\mathbf{k}\] represents a cube, then its volume will be [Roorkee 1988]

    A)             616

    B)             308

    C)             154

    D)             None of these

    Correct Answer: D

    Solution :

                    Volume of cube \[=\,[\mathbf{a}\,\mathbf{b}\,\mathbf{c}]\]                                 \[=\left| \,\begin{matrix}    12 & 4 & 3  \\    8 & -12 & -9  \\    33 & -4 & -24  \\ \end{matrix}\, \right|=12\,\left| \,\begin{matrix}    12 & 1 & 1  \\    8 & -3 & -3  \\    33 & -1 & -8  \\ \end{matrix}\, \right|=3696.\]


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