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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 \[P(3,\,4,\,5),\] \[Q(4,\,6,\,3),\] \[R(-1,\,2,\,4),\] \[S(1,\,0,\,5)\] then the  projection of RS on PQ is [Orissa JEE 2002; RPET 2002]

    A)            ? 2/3

    B)            ? 4/3

    C)            ½

    D)            2

    Correct Answer: B

    Solution :

               Here, \[{{x}_{2}}-{{x}_{\grave{\ }1}}=2,\,{{y}_{2}}-{{y}_{1}}=-2,\,{{z}_{2}}-{{z}_{1}}=1\]            Now, l, m, n for PQ are \[\frac{1}{3},\frac{2}{3},\,\frac{-2}{3}\]            \[\therefore \] Projection of RS on PQ = \[\sum l({{x}_{2}}-{{x}_{1}})\]                                                     = \[\frac{2}{3}-\frac{4}{3}-\frac{2}{3}=\frac{-4}{3}\].


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