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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
    Points (1, 1, 1), (?2, 4, 1), (?1, 5, 5) and (2, 2, 5) are the vertices of a

    A)            Rectangle

    B)            Square

    C)            Parallelogram

    D)            Trapezium

    Correct Answer: B

    Solution :

               Let \[A=(1,\,1,\,1)\];\[B=(-2,\,4,\,1)\];\[C=(-1,\,5,5)\] &\[D=(2,\,2,\,5)\]            \[AB=\sqrt{9+9+0}=3\sqrt{2},\,\,BC=\sqrt{1+1+16}=3\sqrt{2}\] and \[CD=3\sqrt{2}\] and \[AD=3\,\sqrt{2}.\] Hence it is a square.


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