TL;DR: The BAC-CAB vector identity is probably the most important vector identity, and has potentially important applications in introductory physics. I present six coordinate-free derivations of this identity. By “coordinate-free” I mean a derivation that doesn’t rely on any particular coordinate system, and one that relies on the inherent geometric relationships among the vectors involved. […]

Read More Vector Formalism in Introductory Physics II: Six Coordinate-Free Derivations of the BAC-CAB Identity