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IEVref: | 102-04-34 | ID: | |

Language: | en | Status: Standard | |

Term: | tangent plane | ||

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Definition: | at a point of a surface, plane, if it exists, which contains all the tangents at this point to the curves of the surface passing through the point Note 1 to entry: For a surface defined by $r=f(u,\text{\hspace{0.17em}}v)$, where $(u,v)\in \text{U}\subseteq {R}^{\text{2}}$, the tangent plane at point u_{0}, v_{0}) is defined by the vectors ${\left(\frac{\partial f}{\partial u}\right)}_{\begin{array}{l}u={u}_{0}\\ v={v}_{0}\end{array}}$ and ${\left(\frac{\partial f}{\partial v}\right)}_{\begin{array}{c}u={u}_{0}\\ v={v}_{0}\end{array}}$ if they are linearly independent. | ||

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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Note 1 to entry: For a surface defined by $r=f(u,\text{\hspace{0.17em}}v)$, where $(u,v)\in \text{U}\subseteq {R}^{\text{2}}$, the tangent plane at point ** r**(