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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 co-ordinates of the point in which the line joining the points \[(3,\,\ 5,\ -7)\] and \[(-2,\,\ 1,\,\ 8)\] is intersected by the plane yz are given by                                                                      [MP PET 1993]

    A)            \[\left( 0,\,\frac{13}{5},\,\,2 \right)\]

    B)            \[\left( 0,\,-\frac{13}{5},\,-2 \right)\]

    C)            \[\left( 0,-\frac{13}{5},\frac{2}{5} \right)\]

    D)            \[\left( 0,\frac{13}{5},\frac{2}{5} \right)\]

    Correct Answer: A

    Solution :

               Ratio = \[-\left( \frac{3}{-2} \right)=\frac{3}{2}\]            \[\therefore \] Required co-ordinates of the points are,                    \[\,\,\left[ \frac{6-6}{5},\frac{10+3}{5},\frac{-14+24}{5} \right]=\left( 0,\,\frac{13}{5},\,\,2 \right)\].


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