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JCECE Engineering JCECE Engineering Solved Paper-2014

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

    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\[z\] \[\therefore \]  \[\mathbf{x}\cdot (\mathbf{y}\times \mathbf{z})=0\Rightarrow [\mathbf{x}\,\mathbf{y}\,\mathbf{z}]=0\] \[\Rightarrow \]               \[\left| \begin{matrix}    2 & 1 & \alpha   \\    \alpha  & 0 & 1  \\    5 & -1 & 0  \\ \end{matrix} \right|=0\] \[\Rightarrow \]               \[2(0+1)-1(0-5)+\alpha (-\alpha -0)=0\] \[\Rightarrow \]               \[2+5-{{\alpha }^{2}}=0\] \[\Rightarrow \]               \[{{\alpha }^{2}}=7\] \[\Rightarrow \]               \[\alpha =\pm \sqrt{7}\]


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