I think that geometric algebra makes describing rotations quite easy - pick two vectors in the plane you want to rotate, at a suitable angle you desire to rotat

I think that geometric algebra makes describing rotations quite easy - pick two vectors in the plane you want to rotate, at a suitable angle you desire to rotate through - but makes computing them more difficult. In dimensions higher than 2, its always better (in terms of number of multiplications and additions) to use the GA rotor to generate a matrix which applies the rotation. This is the same way that one would use quaternions to track the orientation of an object in a scene, but when the pedal hits the metal you want your graphics card to be doing matrix-vector multiplications to rotate, not quaternion conjugations. GA also makes proving properties about reflections and rotations quite nice, but that’s not usually useful for actual computation (except in a learning environment).