叉乘

In mathematics, the cross product or vector product (occasionally directed area product, to emphasize its geometric significance) is a binary¹ operation on two vectors in a three-dimensional oriented Euclidean vector space (named here E), and is denoted by the symbol $\times$.

c的模：$|c|=|a||b|\sin \theta$
向量积的运算律
分配律

$$(\vec{a}+\vec{b})\times \vec{c}=\vec{a}\times \vec{c}+\vec{b}+\vec{c}$$

数乘结合律

$$(\lambda a)\times b=a\times (\lambda b)=\lambda (a\times b)\text{,其中 }\lambda \text{ 为常数}.$$

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两向量$\vec{a}$和$\vec{b}$的叉积，是一个向量$\vec{c}$

$$\begin{array}{rl}\vec{c}& =\vec{a}\times \vec{b}\\ |\vec{c}|& =|\vec{a}\times \vec{b}|\end{array}$$

$|\vec{c}|$的模长，是以$\vec{a}$、$\vec{b}$为邻边的平行四边形的面积

Footnotes

1. 二元的；有两个不同部分的；Binary describes something that has two different parts. [ADJ n] [Formal] //…a binary star. 双星 ↩