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JEE Main & Advanced Mathematics Three Dimensional Geometry Question Bank System of Co-ordinates, Direction cosines and direction ratios, Projection

  • question_answer
    The point of intersection of the line joining the points (3, 4, 1) and (5, 1, 6) and the xy-plane is

    A)            \[(13,\,23,\,0)\]

    B)            \[\left( \frac{13}{5},\frac{23}{5},0 \right)\]

    C)            (?13, 23, 0)

    D)            \[\left( -\frac{13}{5},\frac{23}{5},0 \right)\]

    Correct Answer: B

    Solution :

               For xy-plane, \[z=0\Rightarrow \frac{6\lambda +1}{\lambda +1}=0\,\,\Rightarrow \,\,\lambda =-\frac{1}{6}\]            \[\therefore \,\,x=\frac{-\,5+18}{5}=\frac{13}{5},\,\,\,y=\frac{-1+24}{5}=\frac{23}{5}\].


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