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

  • question_answer
    The equation of the plane which bisects the line joining the points (?1, 2, 3) and (3, ?5, 6) at right angle, is

    A)            \[4x-7y-3z=8\]

    B)            \[4x+2y-3z=28\]

    C)            \[4x-7y+3z=28\]

    D)            \[4x-7y-3z=28\]

    Correct Answer: C

    Solution :

                       According to question,\[4x-7y+3z=k\]                 ?..(i)            Also, plane (i) passes through \[\left( \frac{-1+3}{2},\,\frac{2-5}{2},\,\frac{3+6}{2} \right)\],  then  \[4+\frac{21}{2}+\frac{27}{2}=k\,\,\,\Rightarrow \,\,k=28\]                    Therefore, required equation is \[4x-7y+3z=28\].


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