The BAC-CAB rule serves as a vital identity in vector calculus, expressing the vector triple product a×(b×c) as the specific linear combination b(a⋅c)−c(a⋅b). According to the sources, this identity is mathematically grounded in the ε−δ relation, which relates the product of two Levi-Civita symbols to a combination of Kronecker deltas. To derive the rule efficiently, one should utilise the symmetries and anti-symmetries of these expressions rather than performing explicit sums for every possible index. Furthermore, the identity can be visually verified through a systematic five-step construction that tracks individual vectors using distinct colours and line styles to demonstrate that the left-hand and right-hand sides ultimately result in the same vector. While mnemonics are a common tool to remember this expansion, our conversation highlights that one should remain attentive to the correct sequence of vectors to ensure the mathematical accuracy of the final expression.
