Orthogonal projection of a point on a line in 3D

Question

Given a point A( 3,2,0) on a plane $\alpha$ = 2x+y-z-8=0 How to find the orthogonal projection of point A on a line r that has a direction vector ( 1,1,1) passes through the origin ? And What are the coordinates of A’ on r

Answer 1

Hint: You need to find $t$ such that with $A'=(t,t,t)$ we have $\vec{AA'} \perp \bf r$, that is $(3-t,\,2-t,\,-t)\cdot(1,1,1)=0$.