# Find the point on the plane $2x - y + 2z = 20$ nearest the origin

What I did was use the distance formula from the plane to the origin, found the normal vector, and found the unit vector of the normal vector. I multiplied the unit vector by the distance to get the point (and it satisfies the equation). Is this correct?

Is there a way of doing this using optimization (i.e. local min/max)?

-
Yes, you can. It will be more work that what you did. –  Ross Millikan Apr 9 '13 at 1:39
Or you can just notice that the normal is $(2, -1, 2)$ and find where the line $(2, -1, 2)t$ intersects your plane. –  user66345 Apr 9 '13 at 1:42