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IEVref:102-03-22ID:
Language:enStatus: backup
Term: component (of a vector quantity)
Synonym1: coordinate (of a vector quantity
[Preferred]
Synonym2:
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Definition: any of the n scalar quantities Q 1 Q 2 Q n MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqk0di9Wr=fpeei0di9v8qiW7rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaaiaadgfadaWgaaWcba GaaGymaaqabaGccaqGSaGaaeiiaiaadgfadaWgaaWcbaGaaGOmaaqa baGccaqGSaGaaeiiaiablAciljaabYcacaqGGaGaamyuamaaBaaale aacaWGUbaabeaaaaa@4369@ in the representation of a vector quantity Q as the linear combination Q 1 a 1 + Q 2 a 2 ++ Q n a n MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqk0di9Wr=fpeei0di9v8qiW7rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaaiaadgfadaWgaaWcba GaaGymaaqabaGccaWHHbWaaSbaaSqaaiaaigdaaeqaaOGaey4kaSIa amyuamaaBaaaleaacaaIYaaabeaakiaahggadaWgaaWcbaGaaGOmaa qabaGccqGHRaWkcqWIMaYscqGHRaWkcaWGrbWaaSbaaSqaaiaad6ga aeqaaOGaaCyyamaaBaaaleaacaWGUbaabeaaaaa@47E3@ of the base vectors a 1 a 2 a n MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqk0di9Wr=fpeei0di9v8qiW7rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaaiaahggadaWgaaWcba qcLbqacaaIXaaaleqaaOGaaeilaiaabccacaWHHbWaaSbaaSqaaKqz aeGaaGOmaaWcbeaakiaabYcacaqGGaGaeSOjGSKaaeilaiaabccaca WHHbWaaSbaaSqaaiaad6gaaeqaaaaa@4499@

NOTE 1 Instead of treating each component of a vector quantity as a quantity (i.e. the product of a numerical value and a unit of measurement), the vector quantity Q may be represented as a vector of numerical values multiplied by the unit:
Q={ Q 1 }[Q] e 1 +{ Q 2 }[Q] e 2 +{ Q 3 }[Q] e 3 =( { Q 1 } e 1 +{ Q 2 } e 2 +{ Q 3 } e 3 )[Q] MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqk0di9Wr=fpeei0di9v8qiW7rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaaiaahgfacqGH9aqpda GadaqaaiaadgfadaWgaaWcbaGaaGymaaqabaaakiaawUhacaGL9baa caaMc8+aamWaaeaacaWGrbaacaGLBbGaayzxaaGaaGPaVlaahwgada WgaaWcbaGaaGymaaqabaGccqGHRaWkdaGadaqaaiaadgfadaWgaaWc baGaaGOmaaqabaaakiaawUhacaGL9baacaaMc8+aamWaaeaacaWGrb aacaGLBbGaayzxaaGaaGPaVlaahwgadaWgaaWcbaGaaGOmaaqabaGc cqGHRaWkdaGadaqaaiaadgfadaWgaaWcbaGaaG4maaqabaaakiaawU hacaGL9baacaaMc8+aamWaaeaacaWGrbaacaGLBbGaayzxaaGaaGPa VlaahwgadaWgaaWcbaGaaG4maaqabaGccqGH9aqpdaqadaqaamaacm aabaGaamyuamaaBaaaleaacaaIXaaabeaaaOGaay5Eaiaaw2haaiaa ykW7caWHLbWaaSbaaSqaaiaaigdaaeqaaOGaey4kaSYaaiWaaeaaca WGrbWaaSbaaSqaaiaaikdaaeqaaaGccaGL7bGaayzFaaGaaGPaVlaa hwgadaWgaaWcbaGaaGOmaaqabaGccqGHRaWkdaGadaqaaiaadgfada WgaaWcbaGaaG4maaqabaaakiaawUhacaGL9baacaaMc8UaaCyzamaa BaaaleaacaaIZaaabeaaaOGaayjkaiaawMcaaiaaykW7daWadaqaai aadgfaaiaawUfacaGLDbaaaaa@7E68@
where { Q 1 },{ Q 2 },{ Q 3 } MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqk0di9Wr=fpeei0di9v8qiW7rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaamaacmaabaGaamyuam aaBaaaleaacaaIXaaabeaaaOGaay5Eaiaaw2haaiaacYcacaaMe8+a aiWaaeaacaWGrbWaaSbaaSqaaiaaikdaaeqaaaGccaGL7bGaayzFaa GaaiilaiaaysW7daGadaqaaiaadgfadaWgaaWcbaGaaG4maaqabaaa kiaawUhacaGL9baaaaa@4932@ are numerical values, [Q] MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqk0di9Wr=fpeei0di9v8qiW7rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaamaadmaabaGaamyuaa Gaay5waiaaw2faaaaa@3B95@ is the unit, and e 1 e 2 e 3   MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqk0di9Wr=fpeei0di9v8qiW7rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaaiaahwgadaWgaaWcba GaaGymaaqabaGccaqGSaGaaeiiaiaahwgadaWgaaWcbaGaaGOmaaqa baGccaqGSaGaaeiiaiaahwgadaWgaaWcbaGaaG4maaqabaGccaqGGa aaaa@41B4@ are the unit vectors. Similar considerations apply to tensor quantities.

NOTE 2 The components of a vector quantity are transformed by a coordinate transformation like the coordinates of a position vector.

NOTE 3 The term "coordinate" is generally used when the vector quantity is a position vector. This usage is consistent with the definition of the coordinates of a vector in mathematics (102-03-09).


Publication date:2007-08
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