# 三维向量的向量积运算公式（B008）

## 选项

[A].   $\vec{a}$ $\times$ $\vec{b}$ $=$ $\begin{vmatrix} x_{1} & z_{1} \\ x_{2} & z_{2} \end{vmatrix} \mathbf{i}$ $-$ $\begin{vmatrix} y_{1} & z_{1} \\ y_{2} & z_{2} \end{vmatrix} \mathbf{j}$ $+$ $\begin{vmatrix} x_{1} & y_{1} \\ x_{2} & y_{2} \end{vmatrix} \mathbf{k}$

[B].   $\vec{a}$ $\times$ $\vec{b}$ $=$ $\begin{vmatrix} y_{1} & z_{1} \\ y_{2} & z_{2} \end{vmatrix} \mathbf{i}$ $+$ $\begin{vmatrix} x_{1} & z_{1} \\ x_{2} & z_{2} \end{vmatrix} \mathbf{j}$ $-$ $\begin{vmatrix} x_{1} & y_{1} \\ x_{2} & y_{2} \end{vmatrix} \mathbf{k}$

[C].   $\vec{a}$ $\times$ $\vec{b}$ $=$ $\begin{vmatrix} y_{1} & z_{1} \\ y_{2} & z_{2} \end{vmatrix} \mathbf{i}$ $+$ $\begin{vmatrix} x_{1} & z_{1} \\ x_{2} & z_{2} \end{vmatrix} \mathbf{j}$ $+$ $\begin{vmatrix} x_{1} & y_{1} \\ x_{2} & y_{2} \end{vmatrix} \mathbf{k}$

[D].   $\vec{a}$ $\times$ $\vec{b}$ $=$ $\begin{vmatrix} y_{1} & z_{1} \\ y_{2} & z_{2} \end{vmatrix} \mathbf{i}$ $-$ $\begin{vmatrix} x_{1} & z_{1} \\ x_{2} & z_{2} \end{vmatrix} \mathbf{j}$ $+$ $\begin{vmatrix} x_{1} & y_{1} \\ x_{2} & y_{2} \end{vmatrix} \mathbf{k}$

$\textcolor{red}{\vec{a}}$ $\textcolor{green}{\times}$ $\textcolor{red}{\vec{b}}$ $=$

$\begin{vmatrix}\mathbf{\textcolor{orange}{i}} & \mathbf{\textcolor{orange}{j}} & \mathbf{\textcolor{orange}{k}} \\ x_{\textcolor{cyan}{1}} & y_{\textcolor{cyan}{1}} & z_{\textcolor{cyan}{1}} \\ x_{\textcolor{blue}{2}} & y_{\textcolor{blue}{2}} & z_{\textcolor{blue}{2}} \end{vmatrix}$ $=$

$\begin{vmatrix} y_{\textcolor{cyan}{1}} & z_{\textcolor{cyan}{1}} \\ y_{\textcolor{blue}{2}} & z_{\textcolor{blue}{2}} \end{vmatrix} \mathbf{\textcolor{orange}{i}}$ $\textcolor{green}{-}$ $\begin{vmatrix} x_{\textcolor{cyan}{1}} & z_{\textcolor{cyan}{1}} \\ x_{\textcolor{blue}{2}} & z_{\textcolor{blue}{2}} \end{vmatrix} \mathbf{\textcolor{orange}{j}}$ $\textcolor{green}{+}$ $\begin{vmatrix} x_{\textcolor{cyan}{1}} & y_{\textcolor{cyan}{1}} \\ x_{\textcolor{blue}{2}} & y_{\textcolor{blue}{2}} \end{vmatrix} \mathbf{\textcolor{orange}{k}}$