Finding a point on a plane closest to another point I have the point $(1,1,1)$ and the plane $2x+2y+z = 0$. I want to find a point that is closest to my point on the plane.
In other words, I want to find a point along the line $(1,1,1)+t(2,2,1)$ but on my plane. Notice that the vector $(2,2,1)$ is my normal vector and therefore I want to find the point parallel to this vector, but from my original point.
I need a nudge to complete this problem! Thank you.

Hint: A general point on the line has the form $(x,y,z) = (1 + 2t, 1 + 2t, 1 + t)$, and for this to be on the plane, it must satisfy the equation of the plane. Plug those in and solve for $t$.
