coords conversion

Hello Math Wizards,
Shortly the thing is: I have a description of the plane in 3D: (Placement and Normal) and a point A which I know is on that plane. The plane is not parallel to X, Y nor Z axis but it contains the [0,0,0] point. Simply what I want to do is to change 3D space coordinates [x,y,z] to [x,y] coordinates on the plane. I will be very grateful for help.


You will need to define x and y axes plus the origin on that plane, otherwise any coordinate given will be meaningless.
When you have all those three necessary informations you are ready to go.
If x and y are orthogonal (ie. xy = 0) all need to do is projecting the vector pointing from the origin to point A on the two axes. If O is the origin of the plane-coordinates and x and y are the axes it’s as easy as
x’ = (A-O)
y’ = (A-O)*(y)/|y|

Thanks for super fast help.