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CET Karnataka Engineering CET - Karnataka Engineering Solved Paper-2002

  • question_answer
    If the vectors \[3\vec{i}+\vec{j}-2\vec{k},\vec{i}+2\vec{j}-3\vec{k},\]\[3\vec{i}+\lambda \vec{j}+5\vec{k}\] are co-planar, the value of is:

    A) \[-4\]                                    

    B) \[4\]

    C)  8                                            

    D)  \[-8\]

    Correct Answer: A

    Solution :

    The vectors are coplanar \[\left| \begin{matrix}    3 & 1 & -2  \\    1 & 2 & -3  \\    3 & \lambda  & 5  \\ \end{matrix} \right|=0\] \[\Rightarrow \]\[3(10+3\pi )-1(5+9)-2(\lambda -6)=0\] \[30+9\lambda -14-2\lambda +12=0\Rightarrow 7\lambda +28=0\] \[\lambda =-4\]


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