Hm, I wonder what the algebra would look like if done with Cl(3)/G(3) operations. I think that would be a great exercise to understand geometric algebra and see

Hm, I wonder what the algebra would look like if done with Cl(3)/G(3) operations. I think that would be a great exercise to understand geometric algebra and see if it's powerful enough (there's a lot of projecting vectors onto planes, which is trivial in that formalism)