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J & K CET Engineering J and K - CET Engineering Solved Paper-2012

  • question_answer
    The vectors \[a=i+4j-7k,\,b=\lambda i-j+4k\] and \[c=-9i+18k\] are coplanar, if \[\lambda \] equals to

    A)  \[0\]               

    B)  \[1\]

    C)  \[2\]               

    D)  None of these

    Correct Answer: D

    Solution :

    Since, given vectors are coplanar. \[\therefore \] \[a\,.\,(b\times c)=0\] \[\Rightarrow \] \[\left| \begin{matrix}    1 & 4 & -7  \\    \lambda  & -1 & 4  \\    -9 & 0 & 18  \\ \end{matrix} \right|=0\] Expanding along \[{{C}_{1}},\] we get \[1(-18-0)-\lambda (72-0)-9(16-7)=0\] \[\Rightarrow \] \[-18-72\lambda -81=0\] \[\Rightarrow \] \[72\lambda =-99\] \[\Rightarrow \] \[\lambda =\frac{-11}{8}\]


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