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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
    If x co-ordinates of a point P of line joining the points \[Q(2,\,2,\,1)\] and \[R\,(5,\,2,-2)\]is 4, then the z-coordinates of P is                                                                     [RPET 2000]

    A)            ? 2

    B)            ?1

    C)            1

    D)            2

    Correct Answer: B

    Solution :

               Suppose P divides QR in the ratio \[\lambda :1\].                    Then co-ordinates of P are \[\left( \frac{5\lambda +2}{\lambda +1},\,\frac{\lambda +2}{\lambda +1},\,\frac{-2\lambda +1}{\lambda +1} \right)\].                    It is given that the x-coordinate of P is 4. i.e.,\[\frac{5\lambda +2}{\lambda +1}=4\]Þ \[\lambda =2\]            So, z-coordinate of P is \[\frac{-2\lambda +1}{\lambda +1}=\frac{-4+1}{2+1}=-1\].


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