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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 lines \[\frac{x-4}{1}=\frac{y-3}{1}=\frac{z-2}{2}\]and \[\frac{x-3}{1}=\frac{y-2}{-4}=\frac{z}{5}\] is

    A)            \[11x-y-3z=35\]

    B)            \[11x+y-3z=35\]

    C)            \[11x-y+3z=35\]

    D)            None of these

    Correct Answer: D

    Solution :

                       \[a\,(x-4)+b\,(y-3)+c\,(z-2)=0\]            \[\therefore \,\,\,a+b+2c=0\] and \[a-4b+5c=0\]            \[\frac{a}{5+8}=\frac{b}{2-5}=\frac{c}{-4-1}=k\]            \[\frac{a}{13}=\frac{b}{-3}=\frac{c}{-5}=k\]            Therefore, the required equation of plane is                          \[-13x+3y+5z+33=0\].


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