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CEE Kerala Engineering CEE Kerala Engineering Solved Paper-2010

  • question_answer
    If the vectors\[\overrightarrow{a}=2\hat{i}+\hat{j}+4\hat{k},\overrightarrow{b}=4\hat{i}-2\hat{j}+3\hat{k}\]and\[\overrightarrow{c}=2\hat{i}-3\hat{j}-\lambda \hat{k}\]are coplanar, then the value of k is equal to

    A)  2                                            

    B)  1

    C)  3                            

    D)         \[-1\]

    E)  0

    Correct Answer: B

    Solution :

    \[\because \]\[\overrightarrow{a}=2\hat{i}+\hat{j}+4\hat{k},\overrightarrow{b}=4\hat{i}-2\hat{j}+3\hat{k}\] and\[\overrightarrow{c}=2\hat{i}-3\hat{j}-\lambda \hat{k}\] are coplaner. Hence,                 \[\left| \begin{matrix}    2 & 1 & 4  \\    4 & -2 & 3  \\    2 & -3 & -\lambda   \\ \end{matrix} \right|=0\] \[\Rightarrow \]               \[2(2\lambda +9)-1(-4\lambda -6)+(-12+4)=0\] \[\Rightarrow \]               \[4\lambda +18+4\lambda +6-48+16=0\] \[\Rightarrow \]               \[8\lambda -8=0\] \[\Rightarrow \]               \[\lambda =1\]


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