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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 co-ordinates of points \[A,B,C,D\]are (a, 2, 1), (1, ?1, 1), (2, ? 3, 4) and (a+1, a+2, a+3) respectively. If \[AB=5\]and \[CD=6\], then \[a=\]

    A)            2

    B)            3

    C)            ? 2

    D)            ? 3

    Correct Answer: D

    Solution :

                \[AB=\sqrt{{{(a-1)}^{2}}+{{3}^{2}}+0}=5\]                    \[\Rightarrow \,\,a-1=\pm \,4\]\[\Rightarrow \,\,a=-3,\,\,5\]            \[CD=\sqrt{{{(a-1)}^{2}}+{{(a+5)}^{2}}+{{(a-1)}^{2}}}=6\]            \[\Rightarrow \,\,{{a}^{2}}-2a-15=0\,\,\Rightarrow \,\,a=-3,\,\,5\]            But common solution of (i) and (ii) is ? 3.


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