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^ ^ deux vecteurs de coordonnées x y ⎛ ⎝⎜ ⎞ ⎠⎟ et x' y' ⎛ ⎝⎜⎠⎟ dans un repère (O, i!, j!). X 1 0. For ordinary 3-space, these vectors may be denoted ı , → e θ y {\displaystyle \exp(\theta v)=\cos \theta +v\sin \theta } , and are not constant in direction. i are often reversed. Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share … Pour les 3 espaces ordinaires, ces vecteurs peuvent être désignés . ( v X φ Un vecteur unitaire est souvent désigné par une lettre minuscule avec un circonflexe , ou "chapeau", comme dans (prononcé "v- chapeau"). It is especially important to note the context of any ordered triplet written in spherical coordinates, as the roles of ^ δ v 1 {\displaystyle \varphi } {\ displaystyle \ exp (\ theta v) = \ cos \ theta + v \ sin \ theta}, Un article de Wikipédia, l'encyclopédie libre, licence Creative Commons Attribution-ShareAlike, Creative Commons Attribution-ShareAlike 3.0 Unported License, Vecteur tangent à une courbe / ligne de flux, Normal à un plan / plan tangent de surface contenant une composante de position radiale et une composante tangentielle angulaire, Perpendiculaire à un axe / une ligne dans une direction radiale, Déviation angulaire possible par rapport à un axe / une ligne, Cette page a été modifiée pour la dernière fois le 12 octobre 2020 à 13:42, This page is based on the copyrighted Wikipedia article. Il est particulièrement important de noter le contexte de tout triplet ordonné écrit en coordonnées sphériques , car les rôles de et sont souvent inversés. + {\ displaystyle \ mathbf {\ hat {e}} _ {\ bot}}. Lv 7. is a versor in the 3-sphere. φ , e z {\ displaystyle \ mathbf {\ hat {\ imath}}} ( s {\ displaystyle \ mathbf {\ hat {e}} _ {1}, \ mathbf {\ hat {e}} _ {2}, \ mathbf {\ hat {e}} _ {3}}, où est le delta de Kronecker (qui vaut 1 pour i = j , et 0 sinon) et est le symbole de Levi-Civita (qui vaut 1 pour les permutations ordonnées comme ijk , et −1 pour les permutations ordonnées comme kji ). {\ displaystyle \ mathbf {\ hat {n}}} ^ The vector elements are roughly equal to [j,j+i,j+2*i,...,j+m*i] where m = fix((k-j)/i).However, if i is not an integer, then floating point arithmetic plays a role in determining whether colon includes the endpoint k in the vector, since k might not be exactly equal to j+m*i.

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