The foot of the perpendicular from (a,b,c) on the line x=y=z is the point (r,r,r) where
r=a+b+c
r=3(a+b+c)
3r=a+b+c
r=4(a+b+c)
Dr s of line is 1,1,1
dr s of line joining (a,b,c)&(r,r,r) isr-a,r-b,r-c
both are perpendicular
1(r-a)+1(r-b)+1(r-c)=0