I don't quite understand what the "center" is supposed to be; in your example, the four points lie in the same plane, and the two vectors are orthogonal, but is it always the case? Then the "center" would be the intersection of (the line going through A and parallel to (CD)) and (the line going through D and parallel to (AB)), is this correct? If so, use the equations of these lines, rather than the equation of a plane: the center can be written for some , this gives you two linear equations (even three) for and , solve them and you are done.