IEC 60050 - International Electrotechnical Vocabulary


IEVref:	102-03-22		ID:
Language:	en		Status: backup

Term:	component (of a vector quantity)
Synonym1:	coordinate (of a vector quantity [Preferred]
Synonym2:
Synonym3:
Symbol:
Definition:	any of the n scalar quantities $Q_{1}, Q_{2}, \dots, Q_{n}$ in the representation of a vector quantity Q as the linear combination $Q_{1} a_{1} + Q_{2} a_{2} + \dots + Q_{n} a_{n}$ of the base vectors $a_{1}, a_{2}, \dots, a_{n}$ 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: $Q = {Q_{1}} [Q] e_{1} + {Q_{2}} [Q] e_{2} + {Q_{3}} [Q] e_{3} = ({Q_{1}} e_{1} + {Q_{2}} e_{2} + {Q_{3}} e_{3}) [Q]$ where ${Q_{1}}, {Q_{2}}, {Q_{3}}$ are numerical values, $[Q]$ is the unit, and $e_{1}, e_{2}, e_{3}$ 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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n Q 1 , Q 2 , …, Q n MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqk0di9Wr=fpeei0di9v8qiW7rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaaiaadgfadaWgaaWcba GaaGymaaqabaGccaqGSaGaaeiiaiaadgfadaWgaaWcbaGaaGOmaaqa baGccaqGSaGaaeiiaiablAciljaabYcacaqGGaGaamyuamaaBaaale aacaWGUbaabeaaaaa@4369@ Q 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@ 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]

where

{Q_{1}}, {Q_{2}}, {Q_{3}}

are numerical values,

[Q]

is the unit, and

e_{1}, e_{2}, e_{3}

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).

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