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May 21 at 2:46 comment added Kapil It is interesting that the quote in the link in another answer by Jacobi indicates that he does not entirely concur.
May 20 at 18:18 comment added Pedro Lauridsen Ribeiro Triple cross products always do in the case of three non-collinear but linearly dependent vectors, that's the point.
May 20 at 16:59 comment added LSpice Re, thanks! I had figured that must be the Jacobi identity in question, but it hadn't occurred to me that the relevant triple cross products would lie back in the original plane, so I hadn't been sure how to interpret it.
May 20 at 16:41 comment added Pedro Lauridsen Ribeiro Unfortunately he doesn't, at least not in this reference... this specific fact refers to the Jacobi identity for the cross (vector) product in $\mathbb{R}^3$. A proper outline of this argument can be found e.g. in khudian.net/Etudes/Geometry/jacidentandheights2.pdf
May 20 at 14:38 history made wiki Post Made Community Wiki by Todd Trimble
May 20 at 13:24 comment added LSpice Does Arnol'd explain why the Jacobi identity forces this geometric consequence?
May 19 at 21:42 history answered Pedro Lauridsen Ribeiro CC BY-SA 4.0