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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 plane \[XOZ\] divides the join of \[(1,\,-1,\,\,5)\] and (2, 3, 4) in the ratio \[\lambda :1\], then \[\lambda \] is [JET 1988]

    A)            ? 3

    B)            3

    C)            \[-\frac{1}{3}\]

    D)            \[\frac{1}{3}\]

    Correct Answer: D

    Solution :

               Since ZOX plane i.e. \[y=0\] divides the join of (1,?1, 5) and (2, 3, 4) in the ratio \[\lambda \,\,:1\].            \[\therefore \,\,\,\frac{3\lambda -1}{\lambda +1}=0\,\,\Rightarrow \,\,\lambda =\frac{1}{3}\].


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