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  • question_answer
    The perpendicular distance of the point (2, 4, ?1) from the line \[\frac{x+5}{1}=\frac{y+3}{4}=\frac{z-6}{-9}\] is [Kurukshetra CEE 1996]

    A)                                                               3

    B)                                                               5

    C)                                                               7

    D)                                                               9

    Correct Answer: C

    Solution :

                     The perpendicular distance of (2, 4, ? 1) from the line \[\frac{x+5}{1}=\frac{y+3}{4}=\frac{z-6}{-9}\] is                 \[\{{{(2+5)}^{2}}+{{(4+3)}^{2}}+(-1-6)\] \[{{\left. -{{\left[ \frac{1(2+5)+4\,(4+3)-9(-1-6)}{\sqrt{1+16+81}} \right]}^{2}} \right\}}^{1/2}}\]                                                                        \[=\sqrt{147-{{\left( \frac{98}{\sqrt{98}} \right)}^{2}}}\]\[=\sqrt{147-98}=\sqrt{49}=7\].


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