Find a point on a plane given the plane's normal and a point along that normal

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I am given a point (Px,Py,Pz) and a normal vector (Nx,Ny,Nz). I have to find the purple point (Tx,Ty,Tz) in this diagram:

illustration http://snag.gy/kLvIZ.jpg

The black line is a plane that intersects the origin (0,0,0) and is perpendicular to the normal. How can I find T?

1
mathgraphicsvector3d

1 Answers

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Hm, I was actually specifically looking for the distance D between P and T. I think the answer to that is simply just dot(N,P). I got there after solving for D in these equations: T=P-N*D and dot(N,T)=0.