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JEE Main & Advanced Sample Paper JEE Main Sample Paper-26

  • question_answer
    The intersection of the planes \[2x-y-3z=8\] and \[x+2y-4z=14\] is the line L. The value of 'a' for which the line L is perpendicular to the line through (a, 2, 2) and (6, 11, -1) is

    A)  10                               

    B)  9

    C)  8                                

    D)  5

    Correct Answer: B

    Solution :

    Let \[\vec{V}\] is the vector along the line of intersection of the planes \[2x-y-3z-8=0\] and \[x+2y-4z-14=0\] then \[V=\left| \begin{matrix}    {\hat{i}} & {\hat{j}} & {\hat{k}}  \\    2 & -1 & -3  \\    1 & 2 & -4  \\ \end{matrix} \right|\,=5(\hat{i}+\hat{j}+\hat{k})\] This is \[\bot \] to join of (a, 2, 2) and (6, 11, -1). Vector \[{{\vec{V}}_{1}}\] along this is, \[{{\vec{V}}_{1}}=(a-6)\hat{i}-9\hat{j}+3\hat{k}\] Now, \[\vec{V}.\,{{\vec{V}}_{1}}=0\] gives a = 9.


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