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@@ -142,13 +142,14 @@ $$
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### 2.5叉积
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#### 2.5.1 定义
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对于两个三维矢量$\vec{a}, \vec{b}$,定义它们的叉积
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$$
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\vec{\boldsymbol a}\times\vec{\boldsymbol b}=\begin{vmatrix}
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$$\begin{aligned}
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\vec{\boldsymbol a}\times\vec{\boldsymbol b}&=\begin{vmatrix}
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\vec{\boldsymbol i}& \vec{\boldsymbol j} & \vec{\boldsymbol k}\cr
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a_x & a_y & a_z \cr
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b_x & b_y & b_z
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\end{vmatrix}=
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(a_yb_z-a_zb_y)\vec{\boldsymbol{i}}+(a_zb_x-a_xb_z)\vec{\boldsymbol{j}}+(a_xb_y-a_yb_x)\vec{\boldsymbol{k}}
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\end{vmatrix}\\
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&=(a_yb_z-a_zb_y)\vec{\boldsymbol{i}}+(a_zb_x-a_xb_z)\vec{\boldsymbol{j}}+(a_xb_y-a_yb_x)\vec{\boldsymbol{k}}
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\end{aligned}
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$$
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#### 2.5.2 叉积的几何意义
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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。
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