Quad from vector

Hi , i'am trying to build a quad from a vector to control its orientation. Basicaly the same idea than building a polygon from an arbitrary normal. I can't do a Cross Product...needs 2 vectors... After some investigations and tests, it looks like a simple rotation matrix will not suffice to drive the other perpendicular vectors needed to retrieve the vertices.

Apparently it is the big jump to quaternions....Can somebody Confirm ?