Vector Projection And Rejection

Vector Projection And Rejection. Both the projection a 1 and rejection a 2 of a vector a are vectors, and their sum is equal to a, which implies that the rejection is given by: 图5 叉积随夹角变化示意图 另外，叉积符合分配律，即 \(\mathbf{a}\times(\mathbf{b}+\mathbf{c})=\mathbf{a}\times\mathbf{b}+\mathbf{a}\times\mathbf{c}\) 。 如图6所示，左图向量b和c都被分解为vector projection和vector rejection两部分，右图则解释了分配律成立的原因，看图时要注意图中的平行四边形和正方形都表示了相等的关系。

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Both the projection a 1 and rejection a 2 of a vector a are vectors, and their sum is equal to a, which implies that the rejection is given by: 图5 叉积随夹角变化示意图 另外，叉积符合分配律，即 \(\mathbf{a}\times(\mathbf{b}+\mathbf{c})=\mathbf{a}\times\mathbf{b}+\mathbf{a}\times\mathbf{c}\) 。 如图6所示，左图向量b和c都被分解为vector projection和vector rejection两部分，右图则解释了分配律成立的原因，看图时要注意图中的平行四边形和正方形都表示了相等的关系。 The vector component or vector resolute of a perpendicular to b, sometimes also called the vector rejection of a from b (denoted ⁡), is the orthogonal projection of a onto the plane (or, in general, hyperplane) orthogonal to b.

Source: vectorified.com

图5 叉积随夹角变化示意图 另外，叉积符合分配律，即 \(\mathbf{a}\times(\mathbf{b}+\mathbf{c})=\mathbf{a}\times\mathbf{b}+\mathbf{a}\times\mathbf{c}\) 。 如图6所示，左图向量b和c都被分解为vector projection和vector rejection两部分，右图则解释了分配律成立的原因，看图时要注意图中的平行四边形和正方形都表示了相等的关系。 The vector component or vector resolute of a perpendicular to b, sometimes also called the vector rejection of a from b (denoted ⁡), is the orthogonal projection of a onto the plane (or, in general, hyperplane) orthogonal to b.

Source: www.jmwww.net

Both the projection a 1 and rejection a 2 of a vector a are vectors, and their sum is equal to a, which implies that the rejection is given by: 图5 叉积随夹角变化示意图 另外，叉积符合分配律，即 \(\mathbf{a}\times(\mathbf{b}+\mathbf{c})=\mathbf{a}\times\mathbf{b}+\mathbf{a}\times\mathbf{c}\) 。 如图6所示，左图向量b和c都被分解为vector projection和vector rejection两部分，右图则解释了分配律成立的原因，看图时要注意图中的平行四边形和正方形都表示了相等的关系。

Source: www.cnblogs.com

Both the projection a 1 and rejection a 2 of a vector a are vectors, and their sum is equal to a, which implies that the rejection is given by: 图5 叉积随夹角变化示意图 另外，叉积符合分配律，即 \(\mathbf{a}\times(\mathbf{b}+\mathbf{c})=\mathbf{a}\times\mathbf{b}+\mathbf{a}\times\mathbf{c}\) 。 如图6所示，左图向量b和c都被分解为vector projection和vector rejection两部分，右图则解释了分配律成立的原因，看图时要注意图中的平行四边形和正方形都表示了相等的关系。

Source: mathematica.stackexchange.com

图5 叉积随夹角变化示意图 另外，叉积符合分配律，即 \(\mathbf{a}\times(\mathbf{b}+\mathbf{c})=\mathbf{a}\times\mathbf{b}+\mathbf{a}\times\mathbf{c}\) 。 如图6所示，左图向量b和c都被分解为vector projection和vector rejection两部分，右图则解释了分配律成立的原因，看图时要注意图中的平行四边形和正方形都表示了相等的关系。 The vector component or vector resolute of a perpendicular to b, sometimes also called the vector rejection of a from b (denoted ⁡), is the orthogonal projection of a onto the plane (or, in general, hyperplane) orthogonal to b.

Source: zhuanlan.zhihu.com

The vector component or vector resolute of a perpendicular to b, sometimes also called the vector rejection of a from b (denoted ⁡), is the orthogonal projection of a onto the plane (or, in general, hyperplane) orthogonal to b. 图5 叉积随夹角变化示意图 另外，叉积符合分配律，即 \(\mathbf{a}\times(\mathbf{b}+\mathbf{c})=\mathbf{a}\times\mathbf{b}+\mathbf{a}\times\mathbf{c}\) 。 如图6所示，左图向量b和c都被分解为vector projection和vector rejection两部分，右图则解释了分配律成立的原因，看图时要注意图中的平行四边形和正方形都表示了相等的关系。

Source: docs.unity3d.com

图5 叉积随夹角变化示意图 另外，叉积符合分配律，即 \(\mathbf{a}\times(\mathbf{b}+\mathbf{c})=\mathbf{a}\times\mathbf{b}+\mathbf{a}\times\mathbf{c}\) 。 如图6所示，左图向量b和c都被分解为vector projection和vector rejection两部分，右图则解释了分配律成立的原因，看图时要注意图中的平行四边形和正方形都表示了相等的关系。 Both the projection a 1 and rejection a 2 of a vector a are vectors, and their sum is equal to a, which implies that the rejection is given by:

Source: id.pinterest.com

图5 叉积随夹角变化示意图 另外，叉积符合分配律，即 \(\mathbf{a}\times(\mathbf{b}+\mathbf{c})=\mathbf{a}\times\mathbf{b}+\mathbf{a}\times\mathbf{c}\) 。 如图6所示，左图向量b和c都被分解为vector projection和vector rejection两部分，右图则解释了分配律成立的原因，看图时要注意图中的平行四边形和正方形都表示了相等的关系。 Both the projection a 1 and rejection a 2 of a vector a are vectors, and their sum is equal to a, which implies that the rejection is given by:

Source: kinematics.com

图5 叉积随夹角变化示意图 另外，叉积符合分配律，即 \(\mathbf{a}\times(\mathbf{b}+\mathbf{c})=\mathbf{a}\times\mathbf{b}+\mathbf{a}\times\mathbf{c}\) 。 如图6所示，左图向量b和c都被分解为vector projection和vector rejection两部分，右图则解释了分配律成立的原因，看图时要注意图中的平行四边形和正方形都表示了相等的关系。 Both the projection a 1 and rejection a 2 of a vector a are vectors, and their sum is equal to a, which implies that the rejection is given by:

The Vector Component Or Vector Resolute Of A Perpendicular To B, Sometimes Also Called The Vector Rejection Of A From B (Denoted ⁡), Is The Orthogonal Projection Of A Onto The Plane (Or, In General, Hyperplane) Orthogonal To B.

Both the projection a 1 and rejection a 2 of a vector a are vectors, and their sum is equal to a, which implies that the rejection is given by: 图5 叉积随夹角变化示意图 另外，叉积符合分配律，即 \(\mathbf{a}\times(\mathbf{b}+\mathbf{c})=\mathbf{a}\times\mathbf{b}+\mathbf{a}\times\mathbf{c}\) 。 如图6所示，左图向量b和c都被分解为vector projection和vector rejection两部分，右图则解释了分配律成立的原因，看图时要注意图中的平行四边形和正方形都表示了相等的关系。