JEE Main & Advanced Mathematics Three Dimensional Geometry Question Bank Line

  • question_answer
    If direction ratios of two lines are \[5,\,\,-12,\,13\] and \[-3,\,4,\,5\] then the angle between them is [RPET 2001]

    A)                                                               \[{{\cos }^{-1}}(1/65)\]

    B)                                                               \[{{\cos }^{-1}}(2/65)\]

    C)                                                               \[{{\cos }^{-1}}(3/65)\]

    D)                                                               \[\pi /2\]

    Correct Answer: A

    Solution :

                    \[\theta ={{\cos }^{-1}}\frac{(-15-48+65)}{\sqrt{25+144+169}\sqrt{9+16+25}}\]           = \[{{\cos }^{-1}}\left( \frac{2}{(13\sqrt{2})\,(5\sqrt{2})} \right)\] = \[{{\cos }^{-1}}\left( \frac{1}{65} \right)\].


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