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JEE Main & Advanced Mathematics Three Dimensional Geometry Question Bank Self Evaluation Test - Introduction to Three Dimensional Geometry

  • question_answer
    A(3, 2, 0), B(5, 3, 2) and C(-9, 6, -3) are the vertices of a triangle ABC. If the bisector of \[\angle ABC\] meets BC at D, then coordinates of D are

    A) \[\left( \frac{19}{8},\frac{57}{16},\frac{17}{16} \right)\]

    B) \[\left( -\frac{19}{8},\frac{57}{16},\frac{17}{16} \right)\]

    C) \[\left( \frac{19}{8},\frac{57}{16},\frac{17}{16} \right)\]

    D) None of these

    Correct Answer: A

    Solution :

    [a] D divides BC in the ratio AB : AC i.e. 3 : 13. Therefore, coordinates of D are \[\left( \frac{3\times -9+13\times 5}{3+13},\frac{3\times 6+13\times 3}{3+13},\frac{3\times -3+13\times 2}{3+13} \right)\] or \[\left( \frac{19}{8},\frac{57}{16},\frac{17}{16} \right)\]


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