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JEE Main & Advanced Mathematics Three Dimensional Geometry Question Bank Line

  • question_answer
    If the lines \[\frac{x-1}{-3}=\frac{y-2}{2k}=\frac{z-3}{2}\], \[\frac{x-1}{3k}=\frac{y-5}{1}=\frac{z-6}{-5}\] are at right angles, then k = [MP PET 1997, 2001]

    A)                                                               ?10

    B)                                                               \[\frac{10}{7}\]

    C)                                                               \[\frac{-10}{7}\]

    D)                                                               \[\frac{-7}{10}\]

    Correct Answer: C

    Solution :

                    Lines are perpendicular if \[{{a}_{1}}{{a}_{2}}+{{b}_{1}}{{b}_{2}}+{{c}_{1}}{{c}_{2}}=0\]                                                               Hence, \[-3\,(3k)+2k\,(1)+2\,(-\,5)=0\,\,\Rightarrow \,\,k=-\frac{10}{7}\].


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