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

  • question_answer
    What will be the volume of that parallelopiped whose sides are a = i ? j + k, b = i ? 3j + 4k and c = 2i ? 5j +  3k [UPSEAT 1999]

    A)             5 unit

    B)             6 unit

    C)             7 unit

    D)             8 unit

    Correct Answer: C

    Solution :

                    Volume of parallelopiped\[=[\mathbf{a}\,\mathbf{b}\,\mathbf{c}]\]     \[=\left| \,\begin{matrix}    1 & -1 & 1  \\    1 & -3 & 4  \\    2 & -5 & 3  \\ \end{matrix}\, \right|\]\[=(-9+20)-(8-3)+(-5+6)\]\[=7\]unit.


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