改进排版

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2025-02-23 20:51:53 +08:00
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@@ -142,13 +142,14 @@ $$
### 2.5叉积
#### 2.5.1 定义
对于两个三维矢量$\vec{a}, \vec{b}$,定义它们的叉积
$$
\vec{\boldsymbol a}\times\vec{\boldsymbol b}=\begin{vmatrix}
$$\begin{aligned}
\vec{\boldsymbol a}\times\vec{\boldsymbol b}&=\begin{vmatrix}
\vec{\boldsymbol i}& \vec{\boldsymbol j} & \vec{\boldsymbol k}\cr
a_x & a_y & a_z \cr
b_x & b_y & b_z
\end{vmatrix}=
(a_yb_z-a_zb_y)\vec{\boldsymbol{i}}+(a_zb_x-a_xb_z)\vec{\boldsymbol{j}}+(a_xb_y-a_yb_x)\vec{\boldsymbol{k}}
\end{vmatrix}\\
&=(a_yb_z-a_zb_y)\vec{\boldsymbol{i}}+(a_zb_x-a_xb_z)\vec{\boldsymbol{j}}+(a_xb_y-a_yb_x)\vec{\boldsymbol{k}}
\end{aligned}
$$
#### 2.5.2 叉积的几何意义
在三维几何中,向量a和向量b的叉乘结果是一个向量,更为熟知的叫法是法向量,该向量垂直于a和b向量构成的平面。