I am looking to find the distance of a line from a point that is normal to a plane. The unit vector of the plane is known, but it does not pass the origin of the coordinate system, and I do not have its scalar equation. Please see attached image.
The coordinates of two points are known, one has a length (L from P1) to the plane along the normal vector, which is also known. I would like the solve for the length (L` from P2 )of the normal vector on the other point (or the coordinates on the plane at the intersection) using the known length(L). Both are normal to the plane.
By using similar triangles I can solve it in 2D by using the unit vector and the distance between the points. See second part of diagram. However, I am somewhat uncertain of how to do it in 3D since the components of the unit vector would have to be accounted for when using the Lengths (L).
I sure there is an easy to solution to this, but I can not seem to get my head around it.