Note 1 to entry: The scalar triple product of three vectors U, V, W is the determinant of the vectors relative to a given orthonormal base:

$\left(U,\text{}V,W\right)=\left|\begin{array}{ccc}{U}_{\text{1}}& U_{\text{2}}& U_{\text{3}}\\ V_{\text{1}}& V_{\text{2}}& V_{\text{3}}\\ W_{\text{1}}& W_{\text{2}}& W_{\text{3}}\end{array}\right|$

Note 2 to entry: The scalar triple product of three position vectors is the volume of the parallelepiped built from the vectors with a sign depending on the space orientation.