The vector triple product uses the BAC-CAB rule: a x (b x c) = b(a.c) - c(a.b). This is different from (a x b) x c = b(a.c) - a(b.c). The result always lies in the plane of the two vectors inside the parentheses. A useful special case is a x (a x b) = (a.b)a - |a|^{2}b, which decomposes b into components parallel and perpendicular to a. The vector triple product is essential for simplifying complex vector expressions in JEE. The key takeaway is that cross product is NOT associative — parentheses matter, and the formulas for a x (b x c) versus (a x b) x c are different.