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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
    If the co-ordinates of the points \[A,B,C\]be \[(-1,\,3,\,2),\,\,(2,\,3,\,5)\] and (3, 5,?2) respectively, then \[\angle A=\]

    A)            \[0{}^\circ \]

    B)            \[45{}^\circ \]

    C)            \[60{}^\circ \]

    D)            \[90{}^\circ \]

    Correct Answer: D

    Solution :

                Equation of AB is \[\frac{x+1}{3}=\frac{y-3}{0}=\frac{z-2}{3}\]    ?..(i)            And that of AC is \[\frac{x+1}{4}=\frac{y-3}{2}=\frac{z-2}{-4}\]       .....(ii)                    Hence\[\angle A={{\cos }^{-1}}\left( \frac{12+0-12}{\sqrt{9+9}\sqrt{16+4+16}} \right)={{90}^{o}}\].


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