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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 O is the origin and \[OP=3\]with direction ratios \[-1,\,2,-2\], then co-ordinates of P are [RPET 2000; DCE 2005]

    A)            (1, 2, 2)

    B)            \[(-1,\,2,\,-2)\]

    C)            (?3, 6, ?9)

    D)            \[(-1/3\,,\,2/3,\,-2/3)\]

    Correct Answer: B

    Solution :

               Co-ordinates of P are \[(lr,\,mr,\,nr)\] Here\[l=\frac{-1}{\sqrt{{{1}^{2}}+{{2}^{2}}+{{2}^{2}}}}=\frac{-1}{3},\,m=\frac{2}{3},\,n=\frac{-2}{3}\] and  \[r=3\,\],   (given)                    \ Co-ordinates of P are (?1, 2, ?2).


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