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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 triangle formed by the points (0, 7, 10), (?1, 6, 6),            (? 4, 9, 6) is         [RPET 2001]

    A)            Equilateral

    B)            Isosceles

    C)            Right angled

    D)            Right angled Isosceles

    Correct Answer: D

    Solution :

               Let A be (0, 7, 10), B (?1, 6, 6) and C (? 4, 9, 6) Then,   \[AB=\sqrt{1+1+16}=\sqrt{18}=3\sqrt{2}\]                        \[BC=\sqrt{9+9+0}=\sqrt{18}=3\sqrt{2}\]                        \[AC=\sqrt{16+4+16}=\sqrt{36}=6\]            Clearly, \[A{{C}^{2}}=A{{B}^{2}}+B{{C}^{2}}\]            Hence \[\Delta \] is right angled. Also, since \[AB=BC\]            \ \[\Delta \] is right angled isosceles.


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