交叉

$$\begin{array}{l}\mathrm{一个}={\mathrm{一个}}_1\widehat{我}+{\mathrm{一个}}_2\hat{j}+{\mathrm{一个}}_3\hat{k},\\ B=b_1\widehat{我}+b_2\hat{j}+b_3\hat{k}。\end{array}$$

$$\begin{array}{l}C=\mathrm{一个}\times B=\left|\begin{array}{cc}\begin{array}{cc}{\widehat{我}}_{}& {\hat{j}}_{}\end{array}& {\hat{k}}_{}\\ \begin{array}{cc}\begin{array}{c}{\mathrm{一个}}_1\\ b_1\end{array}& \begin{array}{c}{\mathrm{一个}}_2\\ b_2\end{array}\end{array}& \begin{array}{c}{\mathrm{一个}}_3\\ b_3\end{array}\end{array}\right|\\ \\ =({\mathrm{一个}}_2{b}_3-{\mathrm{一个}}_3{b}_2)\widehat{我}+({\mathrm{一个}}_3{b}_1-{\mathrm{一个}}_1{b}_3)\hat{j}+({\mathrm{一个}}_1{b}_2-{\mathrm{一个}}_2{b}_1)\hat{k}。\end{array}$$

$$为\mathrm{一个}\times B为=为\mathrm{一个}为为B为罪\alpha 。$$