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

  • question_answer
    The point of intersection of the line \[\frac{x}{1}=\frac{y-1}{2}=\frac{z+2}{3}\] and the  plane \[2x+3y+z=0\]is  [MP PET 1989]

    A)            (0, 1, ?2)

    B)            (1, 2, 3)

    C)            (?1, 9, ?25)

    D)            \[\left( \frac{-1}{11},\frac{9}{11}\frac{-25}{11} \right)\]

    Correct Answer: D

    Solution :

                        \[\frac{x}{1}=\frac{y-1}{2}=\frac{z+2}{3}=r\],  (say)                    So, \[x=r\], \[y=2r+1\], \[z=3r-2\]            \[\therefore \,\,\,2r+3\,(2r+1)+(3r-2)=0\,\,\Rightarrow r=\frac{-1}{11}\]                    Hence, \[x=\frac{-1}{11},\,y=\frac{9}{11},\,\,z=-\frac{25}{11}\].


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