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JEE Main & Advanced Mathematics Three Dimensional Geometry Question Bank Line

  • question_answer
    The length of the perpendicular drawn from the point            (5, 4, ?1) on the line \[\frac{x-1}{2}=\frac{y}{9}=\frac{z}{5}\] is

    A)                                                               \[\sqrt{\frac{110}{2109}}\]

    B)                                                               \[\sqrt{\frac{2109}{110}}\]

    C)                                                               \[\frac{2109}{110}\]

    D)                                                               54

    Correct Answer: B

    Solution :

                     Required distance      \[=\sqrt{{{(5-1)}^{2}}+{{(4-0)}^{2}}+{{(-1-0)}^{2}}-{{\left[ \frac{(5-1)2+(4-0)9+(-1-0)5}{\sqrt{4+81+25}} \right]}^{2}}}\]                                                               \[\sqrt{33-\frac{39\times 39}{110}}=\sqrt{\frac{2109}{110}}\].


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