The foot of the perpendicular from (a,b,c) on the line x=y=z is the point (r,r,r) where

Dr s of line is 1,1,1dr s of line joining (a,b,c)&(r,r,r) isr-a,r-b,r-cboth are perpendicular 1(r-a)+1(r-b)+1(r-c)=0