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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Direction cosine ： ウィキペディア英語版 Direction cosine In analytic geometry, the direction cosines (or directional cosines) of a vector are the cosines of the angles between the vector and the three coordinate axes. Equivalently, they are the contributions of each component of the basis to a unit vector in that direction. ==Three-dimensional Cartesian coordinates == If v is a Euclidean vector in three-dimensional Euclidean space, ℝ3, :$=\; v\_\backslash text\; \backslash mathbf\_\backslash text\; +\; v\_\backslash text\; \backslash mathbf\_\backslash text\; +\; v\_\backslash text\; \backslash mathbf\_\backslash text$ where ex, ey, ez are the standard basis in Cartesian notation, then the direction cosines are :$\backslash begin$ \alpha &= \cos a = \frac^2 + v_\text^2}} ,\\ \beta &= \cos b = \frac^2 + v_\text^2}} ,\\ \gamma &= \cos c = \frac^2 + v_\text^2}}. \end It follows that by squaring each equation and adding the results: :$\backslash cos\; ^2\; a\; +\; \backslash cos\; ^2\; b\; +\; \backslash cos\; ^2\; c\; =\; 1\backslash ,.$ Here, ''α'', ''β'' and ''γ'' are the direction cosines and the Cartesian coordinates of the unit vector v/|v|, and ''a'', ''b'' and ''c'' are the direction angles of the vector v. The direction angles ''a'', ''b'' and ''c'' are acute or obtuse angles, i.e., 0 ≤ ''a'' ≤ π, 0 ≤ ''b'' ≤ ''π'' and 0 ≤ ''c'' ≤ ''π'' and they denote the angles formed between v and the unit basis vectors, ex, ey and ez. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Direction cosine」の詳細全文を読む スポンサード リンク 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.