JEE Main & Advanced Mathematics Three Dimensional Geometry Question Bank Line

  • question_answer
    If the direction ratios of two lines are given by \[3lm-4\,ln+mn=0\] and \[l+2m+3n=0\], then the angle between the lines is [EAMCET 2003]

    A)                                                               \[\pi /2\]

    B)                                                               \[\pi /3\]

    C)                                                               \[\pi /4\]

    D)                                                               \[\pi /6\]

    Correct Answer: A

    Solution :

                     By solving two equations,                 \[({{l}_{1}},\,{{m}_{1}},\,{{n}_{1}})=(2\sqrt{2}-3,\,-\sqrt{2},\,1)\]                 \[({{l}_{2}},\,{{m}_{2}},\,{{n}_{2}})=(-2\sqrt{2}-3,\,\sqrt{2},\,1)\]                 \[{{l}_{1}}{{l}_{2}}+{{m}_{1}}{{m}_{2}}+{{n}_{1}}{{n}_{2}}=0\]                                                                       \  The angle between them is \[\pi /2\].


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