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

  • question_answer
    If the vectors \[2\mathbf{i}-3\mathbf{j}+4\mathbf{k},\,\,\mathbf{i}+2\mathbf{j}-\mathbf{k}\] and \[x\mathbf{i}-\mathbf{j}+2\mathbf{k}\] are coplanar, then \[x=\] [EAMCET 1994]

    A)             \[\frac{8}{5}\]

    B)             \[\frac{5}{8}\]

    C)             0

    D)             1

    Correct Answer: A

    Solution :

                    Given vectors are coplanar,                                 \[\therefore \,\,\,\left| \,\begin{matrix}    2 & -3 & 4  \\    1 & 2 & -1  \\    x & -1 & 2  \\ \end{matrix}\, \right|=0\Rightarrow x=\frac{8}{5}\].


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