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

  • question_answer
    If \[\mathbf{a}=-3\mathbf{i}+7\mathbf{j}+5\mathbf{k},\] \[\mathbf{b}=-3\mathbf{i}+7\mathbf{j}-3\mathbf{k}\], \[\mathbf{c}=7\mathbf{i}-5\mathbf{j}-3\mathbf{k}\] are the three coterminous edges of a parallelopiped, then its volume is [MP PET 1996]

    A)             108

    B)             210

    C)             272

    D)             308

    Correct Answer: C

    Solution :

                    Volume \[=\left| \,\begin{matrix}    -3 & 7 & 5  \\    -3 & 7 & -3  \\    7 & -5 & -3  \\ \end{matrix}\, \right|\]                                 \[=-3\,(-21-15)-7\,(9+21)+5\,(15-49)\]                                 \[=180-210-170=272\].


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