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IEVref: | 102-03-38 | ID: | |

Language: | en | Status: Standard | |

Term: | scalar triple product | ||

Synonym1: | triple product | ||

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Symbol: | |||

Definition: | pseudo-scalar, denoted by (,U,V), assigned to an ordered set of three vectors W, U, V in the three-dimensional Euclidean space, equal to the scalar product $U\cdot (V\times W)$WNote 1 to entry: The scalar triple product of three vectors , V is the determinant of the vectors relative to a given orthonormal base: W$\left(U,\text{}\text{\hspace{0.05em}}\text{\hspace{0.17em}}V,\text{\hspace{0.17em}}W\right)=\left|\begin{array}{ccc}{U}_{\text{1}}& {U}_{\text{2}}& {U}_{\text{3}}\\ {V}_{\text{1}}& {V}_{\text{2}}& {V}_{\text{3}}\\ {W}_{\text{1}}& {W}_{\text{2}}& {W}_{\text{3}}\end{array}\right|$ 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. | ||

Publication date: | 2008-08 | ||

Source: | |||

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Internal notes: | 2017-02-20: Editorial revisions in accordance with the information provided in C00019 (IEV 102) - evaluation. JGO | ||

CO remarks: | |||

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VT remarks: | |||

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Note 1 to entry: The scalar triple product of three vectors ** U**,

$\left(U,\text{}\text{\hspace{0.05em}}\text{\hspace{0.17em}}V,\text{\hspace{0.17em}}W\right)=\left|\begin{array}{ccc}{U}_{\text{1}}& {U}_{\text{2}}& {U}_{\text{3}}\\ {V}_{\text{1}}& {V}_{\text{2}}& {V}_{\text{3}}\\ {W}_{\text{1}}& {W}_{\text{2}}& {W}_{\text{3}}\end{array}\right|$

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.