# Vector calculus: Projection of a point to a plane

1. Feb 8, 2006

### willworkforfood

"The projection of a point P = (x,y,z) to a plane is a point on the plane that is closest to P. If the plane is defined by a point P0 = (x0,y0,z0) and a normal vector n=(x1,y1,z1), computer the projection of P on this plane."

Well, I haven't had a relevant Calculus course in many years, but I'm 99.9% certain that this is a vector calculus problem. My memory is a little sketchy on how to solve for a projection of a point on to a plane, so could anyone here perhaps provide a forumla, algorithm, solution or some other explanation of this problem? Thank you all very much for your time and help even if you don't reply! :)

2. Feb 8, 2006

### 0rthodontist

First find the projection Q of P-P0 onto n. If you think about it geometrically this is the vector connecting P and the closest point on the plane. Then if you take P - Q, you should be able to see that this is the projection of P onto the plane.

3. Feb 8, 2006

### neurocomp2003

its not a vector calculus problem its a 3D mathematics problem or a lin alg problem. You could do either orthodontist method which works good or you can try one of two other methods
[0] you can find teh equation that passes between the point P and projP. Which is easy then substitue back into the plane equation and solve for t.
lot mor work but its worth it
[1] (this is just another way to reword orthodontist, but i think more in lamens terms)
solve for the distance D of P to the plane. which is easy then add a "vector" with length with that distance