(Untitled) | (Untitled) | (Untitled) | (Untitled) | (Untitled) | Examples |

IEVref: | 102-03-22 | ID: | |

Language: | en | Status: backup | |

Term: | component (of a vector quantity) | ||

Synonym1: | coordinate (of a vector quantity [Preferred] | ||

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Definition: | any of the n scalar quantities ${Q}_{1}\text{,}{Q}_{2}\text{,}\dots \text{,}{Q}_{n}$ in the representation of a vector quantity as the linear combination ${Q}_{1}{a}_{1}+{Q}_{2}{a}_{2}+\dots +{Q}_{n}{a}_{n}$ of the base vectors ${a}_{1}\text{,}{a}_{2}\text{,}\dots \text{,}{a}_{n}$QNOTE 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 $Q=\left\{{Q}_{1}\right\}\text{\hspace{0.17em}}\left[Q\right]\text{\hspace{0.17em}}{e}_{1}+\left\{{Q}_{2}\right\}\text{\hspace{0.17em}}\left[Q\right]\text{\hspace{0.17em}}{e}_{2}+\left\{{Q}_{3}\right\}\text{\hspace{0.17em}}\left[Q\right]\text{\hspace{0.17em}}{e}_{3}=\left(\left\{{Q}_{1}\right\}\text{\hspace{0.17em}}{e}_{1}+\left\{{Q}_{2}\right\}\text{\hspace{0.17em}}{e}_{2}+\left\{{Q}_{3}\right\}\text{\hspace{0.17em}}{e}_{3}\right)\text{\hspace{0.17em}}\left[Q\right]$ where $\left\{{Q}_{1}\right\},\text{\hspace{0.17em}}\left\{{Q}_{2}\right\},\text{\hspace{0.17em}}\left\{{Q}_{3}\right\}$ are numerical values, $\left[Q\right]$ is the unit, and ${e}_{1}\text{,}{e}_{2}\text{,}{e}_{3}\text{}$ 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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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:

$Q=\left\{{Q}_{1}\right\}\text{\hspace{0.17em}}\left[Q\right]\text{\hspace{0.17em}}{e}_{1}+\left\{{Q}_{2}\right\}\text{\hspace{0.17em}}\left[Q\right]\text{\hspace{0.17em}}{e}_{2}+\left\{{Q}_{3}\right\}\text{\hspace{0.17em}}\left[Q\right]\text{\hspace{0.17em}}{e}_{3}=\left(\left\{{Q}_{1}\right\}\text{\hspace{0.17em}}{e}_{1}+\left\{{Q}_{2}\right\}\text{\hspace{0.17em}}{e}_{2}+\left\{{Q}_{3}\right\}\text{\hspace{0.17em}}{e}_{3}\right)\text{\hspace{0.17em}}\left[Q\right]$

where $\left\{{Q}_{1}\right\},\text{\hspace{0.17em}}\left\{{Q}_{2}\right\},\text{\hspace{0.17em}}\left\{{Q}_{3}\right\}$ are numerical values, $\left[Q\right]$ is the unit, and ${e}_{1}\text{,}{e}_{2}\text{,}{e}_{3}\text{}$ 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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