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IEVref:102-03-38ID:
Language:enStatus: 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(VW) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqk0di9Wr=fpeei0di9v8qiW7rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaaiaahwfacqGHflY1ca GGOaGaaCOvaiabgEna0kaahEfacaGGPaaaaa@4124@

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:

( U,V,W )=| U 1 U 2 U 3 V 1 V 2 V 3 W 1 W 2 W 3 | MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaamaabmaabaGaaCyvai aacYcacaaMb8UaaGjcVlaaysW7caWHwbGaaiilaiaaysW7caWHxbaa caGLOaGaayzkaaGaeyypa0ZaaqWaaeaafaqabeWadaaabaGaamyvam aaBaaaleaacaqGXaaabeaaaOqaaiaadwfadaWgaaWcbaGaaeOmaaqa baaakeaacaWGvbWaaSbaaSqaaiaabodaaeqaaaGcbaGaamOvamaaBa aaleaacaqGXaaabeaaaOqaaiaadAfadaWgaaWcbaGaaeOmaaqabaaa keaacaWGwbWaaSbaaSqaaiaabodaaeqaaaGcbaGaam4vamaaBaaale aacaqGXaaabeaaaOqaaiaadEfadaWgaaWcbaGaaeOmaaqabaaakeaa caWGxbWaaSbaaSqaaiaabodaaeqaaaaaaOGaay5bSlaawIa7aaaa@553F@

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