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JEE Main & Advanced Mathematics Three Dimensional Geometry Question Bank Critical Thinking

  • question_answer
    The direction cosines of a line segment \[AB\] are \[-2/\sqrt{17},\] \[3/\sqrt{17},\,\,-2/\sqrt{17}.\] If \[AB=\sqrt{17}\] and the co-ordinates of A are (3, -6, 10), then the co-ordinates of B are

    A) (1, -2, 4)

    B) (2, 5, 8)

    C) (-1, 3, -8)

    D) (1, -3, 8)

    Correct Answer: D

    Solution :

    • \[x=3\pm \left( \frac{-2}{\sqrt{17}} \right)\,(\sqrt{17}),\,\,\,y=-\,6\pm \left( \frac{3}{\sqrt{17}} \right)\,(\sqrt{17})\]           
    • and \[z=10\pm \,\left( \frac{-2}{\sqrt{17}} \right)\,\,\,(\sqrt{17})\].           
    • Hence the required co-ordinates are \[(1,\,-3,\,\,8)\] or \[(5,\,\,-9,\,\,12)\].


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