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JEE Main & Advanced Mathematics Three Dimensional Geometry Question Bank Plane

  • question_answer
    The equation of the plane passing through the point  (?1, 3, 2) and perpendicular to each of the planes \[x+2y+3z=5\] and \[3x+3y+z=0\], is

    A)            \[7x-8y+3z-25=0\]

    B)            \[7x-8y+3z+25=0\]

    C)            \[-7x+8y-3z+5=0\]

    D)            \[7x-8y-3z+5=0\]

    Correct Answer: B

    Solution :

               Given, equaiton of plane is passing through the point   (?1, 3, 2)                    \[\therefore \] \[A(x+1)+B(y-3)+C\,(z-2)=0\]   .....(i)                    Since plane (i) is perpendicular to each of the planes \[x+2y+3z=5\] and \[3x+3y+z=0\]                    So, \[A+2B+3C=0\] and \[3A+3B+C=0\]                    \[\therefore \] \[\frac{A}{2-9}=\frac{B}{9-1}=\frac{C}{3-6}=K\]                    Þ \[A=-7K,\,B=8K,\,C=-3K\]                    Put the values of A, B and C in (i)                    we get, \[7x-8y+3z+25=0\], which is the required equation of the plane.


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