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)?
Best Answer
Sounds right.
Yes, you can do this by minimization. First write down the distance of a general point from the origin (hint: it is simple). Then you want to minimize that function subject to the constraint given by the plane.