Is there a geometric "reason" for the Jacobi identity for cross products? Some geometric equality of some area ...?
All proofs I know work by some form of linear algebra (or use the interpretation as a Lie algebra ...)
2026-03-29 08:44:26.1774773866
Geometric Interpretation of Jacobi identity for cross product
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One geometric interpretation is that the altitudes of a triangle intersect in a single point.
You can read about it here: http://olympiads.mccme.ru/lktg/2006/4/ or here: http://www.maths.manchester.ac.uk/~khudian/Etudes/Geometry/jacidentandheights1.pdf