In components (with respect to a right-handed orthonormal basis), if the three vectors are thought of as rows (or columns, but in the same order), the scalar triple product is simply the determinant of the 3-by-3 matrix having the three vectors as rows ( a b c ) = | a 1 a 2 a 3 b 1 b 2 b 3 c 1 c 2 c 3 |