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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 conterminous edges are \[i-j+k,\,\,2i-4j+5k\]and \[3i-5j+2k\] is [Kerala (Engg.) 2002]

    A)             4

    B)             3

    C)             2

    D)             8         

    Correct Answer: D

    Solution :

                    Volume of parallelopiped \[V=[\mathbf{a}\,\mathbf{b}\,\mathbf{c}]\]                                 \[\therefore \,\,V=\left| \,\begin{matrix}    1 & -1 & 1  \\    2 & -4 & 5  \\    3 & -5 & 2  \\ \end{matrix}\, \right|\]                                                \[V=1(-8+25)+1(4-15)+1(-10+12)\]                                   V  \[=17-11+2=8\] unit.


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