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Area Mathematics - General concepts and linear algebra / Vectors and tensors

IEV ref102-03-38

en
scalar triple product
triple product
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(V×W) 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.


fr
produit mixte, m
pseudo-scalaire, noté (U,V,W), attribué à un ensemble ordonné de trois vecteurs U, V, W dans l'espace euclidien à trois dimensions, égal au produit scalaire U(V×W) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqk0di9Wr=fpeei0di9v8qiW7rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaaiaahwfacqGHflY1ca GGOaGaaCOvaiabgEna0kaahEfacaGGPaaaaa@4124@

Note 1 à l'article: Le produit mixte de trois vecteurs U, V, W est le déterminant des vecteurs par rapport à une base orthonormée donnée:

( 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 à l'article: Le produit mixte de trois rayons vecteurs est le volume du parallélépipède construit sur les vecteurs avec un signe qui dépend de l'orientation de l'espace.


de
Spatprodukt, n

es
producto mixto
producto triple escalar

ja
スカラ三重積
三重積

pl
iloczyn mieszany

pt
produto triplo escalar
produto triplo

sr
скаларни троструки производ, м јд
троструки производ, м јд

sv
skalär trippelprodukt

zh
标量三重积
三重积

Publication date: 2008-08
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