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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 dividing the line joining the points \[(1,\,\,2,\,\,3)\]and \[(3,\,\,-5,\,\,6\,)\] in the ratio \[3:\,-5\] is

    A)            \[\left( 2,\,\frac{-25}{2},\,\frac{3}{2} \right)\]

    B)            \[\left( -2,\,\frac{25}{2},\,\frac{-3}{2} \right)\]

    C)            \[\left( 2,\,\,\frac{25}{2},\,\frac{3}{2} \right)\]

    D)            None of these

    Correct Answer: B

    Solution :

               \[x=\frac{-5+9}{-2}=-2,\,\,y=\frac{-5\,(2)+3\,(-5)}{-2}=\frac{25}{2}\]                    \[z=\frac{-5\,(3)+3\,(6)}{-2}=-\frac{3}{2}\].


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