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JEE Main & Advanced JEE Main Paper (Held on 7 May 2012)

  • question_answer
    If \[\vec{a}=\hat{i}-2\hat{j}+3\hat{k},\vec{b}=2\hat{i}+3\hat{j}-\hat{k}\]and\[\vec{c}=\lambda \hat{i}+\hat{j}+(2\lambda -1)\hat{k}\]are coplanar vectors, then\[\lambda \]is equal to

    A) 0      

    B)                        -1

    C)                        2                             

    D)                        1

    Correct Answer: A

    Solution :

                    Since \[\overset{\to }{\mathop{a}}\,=\hat{i}-2\hat{j}+3\hat{k},\overset{\to }{\mathop{b}}\,=2\hat{i}+3j-\hat{k}\]and \[\overset{\to }{\mathop{c}}\,=\lambda \hat{i}+\hat{j}+\left( 2\lambda -1 \right)\hat{k}\]are coplanar therefore \[[\vec{a}\,\vec{b}\,\vec{c}]=0\]i.e.,\[\left| \begin{matrix}    1 & 2 & \lambda   \\    -2 & 3 &1  \\    3 & -1 & 2\lambda -1  \\ \end{matrix} \right|=0\] \[\Rightarrow \]\[1(6\lambda -2)-2(-4\lambda -1)+\lambda (-7)=0\] \[\Rightarrow \]\[(6\lambda -2)-8\lambda +2+2+2\lambda -9\lambda =0\] \[\Rightarrow \]\[7\lambda =0\Rightarrow \lambda =0\]                                


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