I get why these are not vectors. I wonder what is the simplest way to turn them into vectors. One idea I have is to normalize them and convert into X, Y, Z to describe the direction that the plane is facing. Problem is you'd still have to normalize after adding vectors in this space together, so it's not a true vector space.

I get why these are not vectors. I wonder what is the simplest way to turn them into vectors. One idea I have is to normalize them and convert into X, Y, Z to describe the direction that the plane is facing. Problem is you'd still have to normalize after adding vectors in this space together, so it's not a true vector space.

@ Messier-16 Exp maps are your friend.