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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, : where ex, ey, ez are the standard basis in Cartesian notation, then the direction cosines are : It follows that by squaring each equation and adding the results: : 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
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