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

  • question_answer
    The equation of the plane passing through the points         (3,2,2) and (1,0,?1) and parallel to the line \[\frac{x-1}{2}=\frac{y-1}{-2}=\frac{z-2}{3}\], is

    A)            \[4x-y-2z+6=0\]

    B)            \[4x-y+2z+6=0\]

    C)            \[4x-y-2z-6=0\]

    D)            None of these

    Correct Answer: D

    Solution :

                       Equation of plane passing through the point (1,0,?1) is,                    \[a(x-1)+b(y-0)+c(z+1)=0\]       ??(i) Also, plane (i) is passing through (3, 2, 2)                    \[\therefore \]               \[a\,(3-1)+b\,(2-0)+c\,(2+1)=0\]            or  \[2a+2b+3c=0\]                                  ?..(i)            Plane (i) is also parallel to the line\[\frac{x-1}{2}=\frac{y-1}{-2}=\frac{z-2}{3}\]            \[\therefore \]\[2a-2b+3c=0\]                                       ?..(ii)            From (i) and (ii),\[\,\,\frac{a}{-3}=\frac{b}{0}=\frac{c}{2}\]            Therefore, the required plane is,                     \[-3\,(x-1)+0\,(y-0)\,+2\,(z+1)=0\]                    or     \[-\,3x+2z+5=0\].


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