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BCECE Engineering BCECE Engineering Solved Paper-2009

  • question_answer
    The     vectors    \[\vec{a}=\hat{i}+\hat{j}+m\hat{k},\]\[\vec{b}=\hat{i}+\hat{j}+(m+1)\hat{k}\] and \[\vec{c}=\hat{i}-\hat{j}+m\hat{k}\] are coplanar, if \[m\]is equal to

    A)  1                            

    B)         4

    C)  3                            

    D)  no value of m for which vectors are coplanar

    Correct Answer: D

    Solution :

    Given vectors are coplanar, if                 \[\left| \begin{matrix}    1 & 1 & m  \\    1 & 1 & m+1  \\    1 & -1 & m  \\ \end{matrix} \right|=0\] \[\Rightarrow \]\[\left| \begin{matrix}    0 & 0 & -1  \\    1 & 1 & m+1  \\    1 & -1 & m  \\ \end{matrix} \right|=0\]                              \[[{{R}_{1}}\to {{R}_{1}}-{{R}_{2}}]\] \[\Rightarrow \]\[-1(-1-1)=0\] \[\Rightarrow \]\[2\ne 0\] \[\therefore \]No value of m for which vectors are coplanar.


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