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IEVref: | 102-05-07 | ID: | |

Language: | en | Status: Standard | |

Term: | vector surface element | ||

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Definition: | in the three-dimensional Euclidean space, vector normal to a given surface at a given point, the magnitude of which is the scalar surface element at the given point Note 1 to entry: When the space orientation is defined by a right-handed trihedron, the direction of the vector surface element defines the orientation of the surface at that point as being in the anti-clockwise direction for an observer looking in the direction opposite to that of the vector. Note 2 to entry: For a surface defined by (fu, v) where $(u,v)\in \text{U}\subseteq {R}^{\text{2}}$, the vector surface element is given by $\frac{\partial f}{\partial u}\times \frac{\partial f}{\partial v}\cdot \mathrm{d}u\mathrm{d}v$. Note 3 to entry: A vector surface element is preferably designated by ${e}_{\text{n}}\mathrm{d}A$ or sometimes by $n\mathrm{d}A$, where ${e}_{\text{n}}=n$ is a unit vector normal to the surface and d | ||

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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VT remarks: | |||

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Domain5: |

Note 1 to entry: When the space orientation is defined by a right-handed trihedron, the direction of the vector surface element defines the orientation of the surface at that point as being in the anti-clockwise direction for an observer looking in the direction opposite to that of the vector.

Note 2 to entry: For a surface defined by ** r** =

$\frac{\partial f}{\partial u}\times \frac{\partial f}{\partial v}\cdot \mathrm{d}u\mathrm{d}v$.

Note 3 to entry: A vector surface element is preferably designated by ${e}_{\text{n}}\mathrm{d}A$ or sometimes by $n\mathrm{d}A$, where ${e}_{\text{n}}=n$ is a unit vector normal to the surface and d*A* is a scalar surface element.