The scalar triple product [a b c] = a.(b x c) equals the determinant |$a_{1}$ $a_{2}$ $a_{3}$; $b_{1}$ $b_{2}$ $b_{3}$; $c_{1}$ $c_{2}$ $c_{3}$|. Properties: (1) Cyclic permutation preserves value: [a b c] = [b c a] = [c a b]. (2) Swapping two vectors changes sign: [a b c] = -[b a c]. (3) |[a b c]| = volume of parallelepiped formed by the three vectors. (4) Volume of tetrahedron = $\frac{1}{6}$|[a b c]|. (5) [a b c] = 0 iff a, b, c are coplanar.