First slide
Straight lines in 3D
Question

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

Moderate
Solution

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

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