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

  • question_answer
    If the vectors \[2\mathbf{i}+\mathbf{j}-\mathbf{k},\,-\mathbf{i}+2\mathbf{j}+\lambda \mathbf{k}\] and  \[-5\mathbf{i}+2\mathbf{j}-\mathbf{k}\] are coplanar, then the value of \[\lambda \] is equal             [J & K 2005]

    A)             ? 13

    B)             13/9

    C)             ? 13/9

    D)             ? 9/13

    Correct Answer: C

    Solution :

                    Given vectors are coplanar                                 \[\therefore \]  \[\left| \begin{matrix}    2 & 1 & -1  \\    -1 & 2 & \lambda   \\    -5 & 2 & -1  \\ \end{matrix} \right|=0\]                                 Þ \[-4-4\lambda -5\lambda -1-8=0\]                                 Þ \[-9\lambda -13=0\] Þ \[\lambda =\frac{-13}{9}\].


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