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J & K CET Engineering J and K - CET Engineering Solved Paper-2006

  • question_answer
    If the vectors \[2\hat{i}-3\hat{j}+4\hat{k},\,\,\hat{i}+2\hat{j}-\hat{k}\] and \[\lambda \hat{i}-\hat{j}+2\hat{k}\]are coplanar, then X is equal to

    A)  \[0\]

    B)  \[5/8\]

    C)  \[8/5\]

    D)  \[1\]

    Correct Answer: C

    Solution :

    Vectors are coplanar, if \[\vec{a}.(\vec{b}\times \vec{c})=0\] ie, \[\left| \begin{matrix}    2 & -3 & 4  \\    1 & 2 & -1  \\    \lambda  & -1 & 2  \\ \end{matrix} \right|=0\] \[\Rightarrow \]  \[2(4-1)+3(2+\lambda )+4(-1-2\lambda )=0\] \[\Rightarrow \] \[6+6+3\lambda -4-8\lambda =0\] \[\Rightarrow \] \[-5\lambda =-8\] \[\Rightarrow \] \[\lambda =\frac{8}{5}\]


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