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JEE Main & Advanced Sample Paper JEE Main Sample Paper-32

  • question_answer
    If the lines \[\frac{x-2}{1}=\frac{y-3}{1}=\frac{z-4}{-k}\]and \[\frac{x-1}{k}=\frac{y-4}{2}=\frac{z-5}{1}\]are coplanar, then the sum of all possible values of k is

    A) \[-3\]             

    B)   3

    C) \[-4\]                

    D) 4

    Correct Answer: A

    Solution :

    The given lines are coplanar if \[\left| \begin{matrix}    2-1 & 3-4 & 4-5  \\    1 & 1 & -k  \\    k & 2 & 1  \\ \end{matrix} \right|=\left| \begin{matrix}    1 & -1 & -1  \\    1 & 1 & -k  \\    k & 2 & 1  \\ \end{matrix} \right|\] \[=\left| \begin{matrix}    1 & 0 & 0  \\    1 & 2 & 1-k  \\    k & k+2 & 1+k  \\ \end{matrix} \right|\] or if  \[2(1+k)-(k-2)(1-k)=0\] if \[{{k}^{2}}+3k=0\] or if \[k=0\] or \[-3\]


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