IEVref: 102-05-07 ID: Language: en Status: Standard Term: vector surface element Synonym1: Synonym2: Synonym3: Symbol: 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 pointNote 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 = f(u, v) where $\left(u,v\right)\in \text{U}\subseteq {R}^{\text{2}}$, the vector surface element is given by $\frac{\partial f}{\partial u}×\frac{\partial f}{\partial v}\cdot \mathrm{d}u\mathrm{d}v$. 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 dA is a scalar surface element. Publication date: 2008-08 Source: Replaces: Internal notes: 2017-02-20: Editorial revisions in accordance with the information provided in C00019 (IEV 102) - evaluation. JGO CO remarks: TC/SC remarks: VT remarks: Domain1: Domain2: Domain3: Domain4: Domain5: