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

  • question_answer
    If \[\mathbf{a}=\mathbf{i}-\mathbf{j}+\mathbf{k},\,\,\mathbf{b}=\mathbf{i}+2\mathbf{j}-\mathbf{k}\] and \[\mathbf{c}=3\mathbf{i}+p\mathbf{j}+5\mathbf{k}\] are coplanar then the value of p will be     [RPET 1985, 86, 88, 91]

    A)             ? 6

    B)             ? 2

    C)             2

    D)             6

    Correct Answer: A

    Solution :

                    \[\left| \,\begin{matrix}    1 & -1 & 1  \\    1 & 2 & -1  \\    3 & p & 5  \\ \end{matrix}\, \right|=0\Rightarrow p=-6.\]


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