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 equation of line passing through M−3,5,2 and making equal angles with coordinate axes is x+31=y−51=z−21General point on the above line isPk−3,k+5,k+2If the perpendicular distance from  A−2,3,1 to the above line is AP  then  APis perpendicular to the line  x+31=y−51=z−21Hence, k−1⋅1+k+2⋅1+k+1⋅1=03k+2=0k=−23 Hence the point  Pk−3,k+5,k+2 is P−113,−135,−43The required distance is AP,  AP=259+169+19=143