JEE Main & Advanced Mathematics Three Dimensional Geometry Question Bank Line

  • question_answer
    If the co-ordinates of the points A, B, C, D be (1, 2, 3),         (4, 5, 7), (?4, 3, ?6) and (2, 9, 2) respectively, then the angle between the lines AB and CD is

    A)                                                               \[\frac{\pi }{6}\]

    B)                                                               \[\frac{\pi }{4}\]

    C)                                                               \[\frac{\pi }{3}\]

    D)                                                               None of these

    Correct Answer: D

    Solution :

                     Here, d.r.'s of line AB and CD are 3, 3, 4 and 6, 6, 8 respectively.                                                                    \[\therefore \]\[\theta ={{\cos }^{-1}}\left[ \frac{(3)\,(6)+(3)\,(6)+(4)\,(8)}{\sqrt{34}.\,\sqrt{136}} \right]={{\cos }^{-1}}\,\left[ \frac{68}{2\times 34} \right]={{0}^{o}}\].


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