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JEE Main & Advanced Mathematics Three Dimensional Geometry Question Bank Plane

  • question_answer
    The equation of the plane through the three points (1, 1, 1), (1, ?1, 1) and (?7,?3,?5), is [AISSE 1984]

    A)            \[3x-4z+1=0\]

    B)            \[3x-4y+1=0\]

    C)            \[3x+4y+1=0\]

    D)            None of these

    Correct Answer: A

    Solution :

               Plane passing through (1, 1, 1) is  \[a\,(x-1)+b\,(y-1)+c\,(z-1)=0\]            It also passes through (1, ? 1, 1) and (?7, ? 3, ? 5), then \[b=0,\,\,a=-\frac{3}{4}c\]            Hence the required equation is \[3x-4z+1=0\].            Trick : Since the plane \[3x-4z+1=0\] passes through given three points.


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