Relative UV coordinates on a plane

Hey all.

I’m trying to simulate some kind of POV effect on a light installation, but I can feel that my math is a bit rusty. I use the ofxRay addon and have rays intersecting a plane. This function returns an ofVec3f, which is the world coordinates for the intersection of each ray. I do however need the coordinates (u v) on the plane itself - regardless of where it is placed.

Can someone give a quick hint or guide to how this can be done?

Best regards,
Frederik