JEE Main & Advanced Mathematics Three Dimensional Geometry Question Bank Line and Plane

  • question_answer
    The co-ordinates of the point where the line \[\frac{x-6}{-1}=\frac{y+1}{0}=\frac{z+3}{4}\] meets the plane \[x+y-z=3\]are [MP PET 1998; Pb. CET 2002]

    A)            (2, 1, 0)

    B)            (7, ?1, ?7)

    C)            (1, 2, ?6)

    D)            (5, ?1, 1)

    Correct Answer: D

    Solution :

                       Point on the line, \[\frac{x-6}{-1}=\frac{y+1}{0}=\frac{z+3}{4}=r\] are \[(-\,r+6,\,\,-1,\,\,4r-3)\]            This will be satisfy plane \[x+y-z=3\]            \[\therefore \,\,-r+6-1-4r+3=3\,\,\Rightarrow \,\,-5r+5=0\]\[\Rightarrow \,\,r=1\]            Required co-ordinates of point \[\equiv \,(5,\,\,-1,\,\,1)\].


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