JEE Main & Advanced Mathematics Three Dimensional Geometry Question Bank Plane

  • question_answer
    The equation of the plane which bisects the angle between the planes \[3x-6y+2z+5=0\] and \[4x-12y+3z-3=0\] which contains the origin is

    A)            \[33x-13y+32z+45=0\]

    B)            \[x-3y+z-5=0\]

    C)            \[33x+13y+32z+45=0\]

    D)            None of these

    Correct Answer: D

    Solution :

               Equation of plane bisecting the angle containing origin is (making constant term of same sign)            \[\frac{-3x+6y-2z-5}{\sqrt{{{3}^{2}}+{{6}^{2}}+{{2}^{2}}}}=+\left[ \frac{4x-12y+3z-3}{\sqrt{{{4}^{2}}+{{12}^{2}}+{{3}^{2}}}} \right]\]            or  \[\frac{-3x+6y-2z-5}{7}=\frac{4x-12y+3z-3}{13}\]            or   \[67x-162y+47z+44=0\].


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