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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 points (5, ? 4, 2), (4, ?3, 1), (7, ? 6, 4) and (8, ?7, 5) are the vertices of [RPET 2002]

    A)            A rectangle

    B)            A square

    C)            A parallelogram

    D)            None of these

    Correct Answer: D

    Solution :

               Let \[A(5,\,-4,\,2)\],\[B(4,\,-3,\,1),\]\[C(7,\,-6,\,4)\]            and \[D(8,\,-7,\,5)\]. Then \[AB=\sqrt{1+1+1}=\sqrt{3}\],            \[BC=\sqrt{9+9+9}=3\sqrt{3}\], \[CD=\sqrt{1+1+1}=\sqrt{3}\]                    \[AD=\sqrt{9+9+9}=3\sqrt{3}\].                    But \[\overrightarrow{AB}\,.\,\overrightarrow{BC}\ne 0\]            Let the angle between AB and BC be \[\theta \], then \[\cos \theta =-1\Rightarrow \theta =\pi \]. Hence option  is correct.


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