Yes, a Gibbs/Heaviside “pseudovector” (a.k.a. “axial vector”) is actually a bivector – a magnitude with a planar orientation, rather than linear orientation. Qu

Yes, a Gibbs/Heaviside “pseudovector” (a.k.a. “axial vector”) is actually a bivector – a magnitude with a planar orientation, rather than linear orientation. Quantities representing a rotation are naturally oriented with a plane of rotation; there is only a unique perpendicular linear “axis” of rotation in 3d space (e.g. in 4D, the subspace fixed under a simple plane-oriented rotation is a perpendicular plane). When you properly treat bivectors as bivectors instead of cramming both bivectors and vectors down into one type of object, all of the trickiness about sign flips under reflection etc. go away. Almost every time you see a cross product in a formula, you should really have a wedge product, and the result should be a bivector. In GA, vector identities all generalize cleanly to any dimension (the trick of representing bivectors as vectors only works in 3D). See http://geocalc.clas.asu.edu/pdf/OerstedMedalLecture.pdf http://geocalc.clas.asu.edu/pdf/OerstedMedalLecture.pdf