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JEE Main & Advanced Mathematics Three Dimensional Geometry Question Bank Self Evaluation Test - Three Dimensional Geometry

  • question_answer
    Given the line \[L:\frac{x-1}{3}=\frac{y+1}{2}=\frac{z-3}{-1}\]  and the plane\[\pi :x-2y=z\]. of the following assertions, the only one that is always true is

    A) L is \[\bot \] to \[\pi \]

    B) L lies in \[\pi \]

    C) L is paralel to \[\pi \]

    D) None of these

    Correct Answer: B

    Solution :

    [b] Since \[3(1)+2(-2)+(-1)(-1)=3-4+1=0\] \[\therefore \] Given line is \[\bot \] to the normal to the plane i.e., given line is parallel to the given plane. Also \[(1,-1,3)\] lies on the plane \[x-2y-z=0\]if \[1-2(-1)-3=0\] i.e. \[1+2-3=0\] Which is true \[\therefore \] L lies in plane\[\pi \].


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