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JEE Main & Advanced Mathematics Vector Algebra Question Bank Critical Thinking

  • question_answer
    If \[\mathbf{x}\] is parallel to \[\mathbf{y}\] and \[\mathbf{z}\] where \[\mathbf{x}=2\mathbf{i}+\mathbf{j}+\alpha \mathbf{k}\], \[\mathbf{y}=\alpha \mathbf{i}+\mathbf{k}\] and \[\mathbf{z}=5\mathbf{i}-\mathbf{j}\], then \[\alpha \] is equal to [J & K 2005]

    A) \[\pm \sqrt{5}\]

    B) \[\pm \sqrt{6}\]

    C) \[\pm \sqrt{7}\]

    D) None of these

    Correct Answer: C

    Solution :

    • Given x is parallel to y and z                   
    • \[\therefore \] \[\mathbf{x}\,.\,(\mathbf{y}\times \mathbf{z})=0\] \[\Rightarrow \] \[[\mathbf{x}\,\,\mathbf{y}\,\,\mathbf{z}]=0\]                   
    • Þ \[\left| \,\begin{matrix}    2 & 1 & \alpha   \\    \alpha  & 0 & 1  \\    5 & -1 & 0  \\ \end{matrix}\, \right|=0\Rightarrow \alpha =\pm \,\sqrt{7}\].


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