翻訳と辞書 Words near each other ・ Copiula major ・ Copiula minor ・ Copiula obsti ・ Copiula oxyrhina ・ Copiula pipiens ・ Copiula tyleri ・ Copium ・ Copivaleria ・ Copivaleria grotei ・ Copkiller ・ Copla ・ Copla (meter) ・ Copla (music) ・ Coplan Saves His Skin ・ Coplanar waveguide ・ Coplanarity ・ Copland ・ Copland (company) ・ Copland (crater) ・ Copland (operating system) ・ Copland (surname) ・ Copland Coal ・ Copland College ・ Copland Pass ・ Copland Pass (Antarctica) ・ Copland Peak ・ Copland River ・ Copland's rock frog ・ Coplas de Purim ・ Coplay Cement Company Kilns Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Coplanarity ： ウィキペディア英語版 Coplanarity In geometry, a set of points in space are coplanar if there exists a geometric plane that contains them all. For example, three points are always coplanar, and if the points are distinct and non-collinear, the plane they determine is unique. However, a set of four or more distinct points will, in general, not lie in a single plane. Two lines in three-dimensional space are coplanar if there is a plane that includes them both. This occurs if the lines are parallel, or if they intersect each other. Two lines that are not coplanar are called skew lines. Distance geometry provides a solution technique for the problem of determining whether a set of points is coplanar, knowing only the distances between them. ==Properties== In three-dimensional space, two independent vectors with the same initial point determine a plane through that point. Their cross product is a normal vector to that plane, and any vector orthogonal to this cross product through the initial point will lie in the plane. This leads to the following coplanarity test. Four distinct points, ''x''1, ''x''2, ''x''3 and ''x''4 are coplanar if and only if, :$(x\_3\; -\; x\_1)\; \backslash cdot\; (-\; x\_1)\; \backslash times\; (x\_4\; -\; x\_3))\; =\; 0.$ If three vectors $\backslash mathbf,\; \backslash mathbf$ and $\backslash mathbf$ are coplanar, then :$(\backslash mathbf\backslash cdot\backslash mathbf)\backslash mathbf\; +\; (\backslash mathbf\backslash cdot\backslash mathbf)\backslash mathbf\; =\; \backslash mathbf,$ where $\backslash mathbf$ denotes the unit vector in the direction of $\backslash mathbf$. That is, the vector projections of $\backslash mathbf$ on $\backslash mathbf$ and $\backslash mathbf$ on $\backslash mathbf$ add to give the original $\backslash mathbf$. 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.