You have just made my point for me. There is no such concept as a " a space (non-planar) quadrilateral".

This question has appeared in most of the vector approach to geometry text I have reviewed.

It is usually more carefully worded:Given four points, no three of which are colinear, six vectors can be determined. If any pair of those vectors are parallel and have same length then the four points are the vertices of a parallelogram.

That is my sentiment about your contribution exactly.