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

  • question_answer
    If the vectors \[2\mathbf{i}-\mathbf{j}+\mathbf{k},\,\,\mathbf{i}+2\mathbf{j}-3\mathbf{k}\] and \[3\mathbf{i}+\lambda \mathbf{j}+5\mathbf{k}\] be coplanar, then \[\lambda =\]             [Roorkee 1986; RPET 1999, 02; Kurukshetra CEE 2002]

    A)             ? 1

    B)             ? 2

    C)             ? 3

    D)             ? 4

    Correct Answer: D

    Solution :

                    If the given vectors are coplanar, then their scalar triple product is zero. \[\left| \begin{matrix}    2 & -1 & 1  \\    1 & 2 & -3  \\    3 & \lambda  & 5  \\ \end{matrix} \right|=0\Rightarrow \lambda =-4.\]


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