The vector triple product is: a x (b x c) = b(a.c) - c(a.b) — the "BAC-CAB" rule. Note: the outer vector a distributes its dot products to b and c. Similarly: (a x b) x c = b(a.c) - a(b.c) (different formula — parentheses matter since cross product is not associative). The result always lies in the plane of the two vectors inside the parentheses. This identity is essential for simplifying complex vector expressions in JEE.