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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 Vector projection ： ウィキペディア英語版 Vector projection The vector projection of a vector a on (or onto) a nonzero vector b (also known as the vector component or vector resolute of a in the direction of b) is the orthogonal projection of a onto a straight line parallel to b. It is a vector parallel to b, defined as :$\backslash mathbf\_1\; =\; a\_1\backslash mathbf\backslash ,$ where $a\_1$ is a scalar, called the scalar projection of a onto b, and b̂ is the unit vector in the direction of b. In turn, the scalar projection is defined as :$a\_1\; =\; |\backslash mathbf|\backslash cos\backslash theta\; =\; \backslash mathbf\backslash cdot\backslash mathbf\; =\; \backslash mathbf\backslash cdot\backslash frac|\}\backslash ,$ where the operator · denotes a dot product, |a| is the length of a, and ''θ'' is the angle between a and b. The scalar projection is equal to the length of the vector projection, with a minus sign if the direction of the projection is opposite to the direction of b. The vector component or vector resolute of a perpendicular to b, sometimes also called the vector rejection of a ''from'' b,〔 G. Perwass, 2009. (Geometric Algebra With Applications in Engineering ), p. 83.〕 is the orthogonal projection of a onto the plane (or, in general, hyperplane) orthogonal to b. Both the projection a1 and rejection a2 of a vector a are vectors, and their sum is equal to a, which implies that the rejection is given by :$\backslash mathbf\_2\; =\; \backslash mathbf\; -\; \backslash mathbf\_1.$ ==Notation== Typically, a vector projection is denoted in a bold font (e.g. a1), and the corresponding scalar projection with normal font (e.g. ''a''1). In some cases, especially in handwriting, the vector projection is also denoted using a diacritic above or below the letter (e.g., $\backslash vec\_1$ or ''a''1; see Euclidean vector representations for more details). The vector projection of a on b and the corresponding rejection are sometimes denoted by a∥b and a⊥b, respectively. 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「Vector projection」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.