The distance of a point A−2,3,1 from the line  MN→ throughM−3,5,2 , which makes equal angles with the coordinate axes is

The distance of a point A2,3,1 from the line  MN throughM3,5,2 , which makes equal angles with the coordinate axes is

  1. A

    163

  2. B

    143

  3. C

    23

  4. D

    53

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    Solution:

    The equation of line passing through M3,5,2 and making equal angles with coordinate axes is x+31=y51=z21

    General point on the above line isPk3,k+5,k+2

    If the perpendicular distance from  A2,3,1 to the above line is AP  then  APis perpendicular to the line  x+31=y51=z21

    Hence, 

    k11+k+21+k+11=03k+2=0k=23

     Hence the point  Pk3,k+5,k+2 is P113,135,43

    The required distance is AP,  AP=259+169+19=143

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