I don't quite understand what you're asking for. But you're trying to find the plane in which the quad is in right? For a plane you need two vectors or three points if you don't have defined vectors (a triangle).

Say that you have p1 (0,2,0) p2 (1,0,0) p3 (0,1,0) that you know they're in your quad and that at least two of them aren't multiples of each other. You'd make two vectors from them by selecting one point as the begining of the two vectors, and the other points as the end of those vectors.

Say p1 is the beggining. p2-p1 = v1 = (1,-2,0). p3-p1 = v2 = (0,-1,0). v1 and v2 represent your plane. Make the cross product between them and you have your orthogonal vector that represents your axis.

You can normalize it and displace it by the same amount that the quad is displaced if you need it centered on your quad.

There is more to it (like finding the equation of the plane for example) but I don't remember much more of the algebra classes i took