The scalar triple product [a b c] = a . (b x c) equals the determinant of the 3x3 matrix formed by the components. Its absolute value gives the volume of the parallelepiped formed by the three vectors, and $\frac{1}{6}$|[a b c]| gives the tetrahedron volume. Key properties: cyclic permutation preserves value ([a b c] = [b c a] = [c a b]), while swapping two vectors changes the sign. Scalars factor out: [ka b c] = k[a b c]. The triple product is zero iff the vectors are coplanar — this is the primary coplanarity test in JEE. For four points, coplanarity is tested as [AB AC AD] = 0. Important identity: [a+b, b+c, c+a] = 2[a b c], and [a-b, b-c, c-a] = 0.