I have 2 vectors, U1 and V1 (from origin) in 3D space, together forming a plane P1. The vectors then both changes to U2 and V2 (still from origin) forming a new plane P2. Is there there a way to obtain the quaternion representing the rotation between P1 and P2?
I'll just post the full answer thanks to Shiyu in the comments. I'm an engineer and programmer, so the writing is probably not the way a mathematician would want to read it.