IEVref: 102-03-38 ID: Language: en Status: Standard Term: scalar triple product Synonym1: triple product Synonym2: Synonym3: Symbol: Definition: pseudo-scalar, denoted by (U,V,W), assigned to an ordered set of three vectors U, V, W in the three-dimensional Euclidean space, equal to the scalar product $U\cdot \left(V×W\right)$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: $\left(U,\text{​}\text{ }\text{\hspace{0.17em}}V,\text{\hspace{0.17em}}W\right)=|\begin{array}{ccc}{U}_{\text{1}}& {U}_{\text{2}}& {U}_{\text{3}}\\ {V}_{\text{1}}& {V}_{\text{2}}& {V}_{\text{3}}\\ {W}_{\text{1}}& {W}_{\text{2}}& {W}_{\text{3}}\end{array}|$ 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. Publication date: 2008-08 Source: Replaces: Internal notes: 2017-02-20: Editorial revisions in accordance with the information provided in C00019 (IEV 102) - evaluation. JGO CO remarks: TC/SC remarks: VT remarks: Domain1: Domain2: Domain3: Domain4: Domain5: