$$\begin{array}{l}\mathrm{一个}={\mathrm{一个}}_1\widehat{我}+{\mathrm{一个}}_2\hat{j}+{\mathrm{一个}}_{3.}\hat{k},\\ B=b_1\widehat{我}+b_2\hat{j}+b_{3.}\hat{k}。\end{array}$$

$$\begin{array}{l}C=\mathrm{一个}\times B=\left|\begin{array}{cc}\begin{array}{cc}{\widehat{我}}_{}& {\hat{j}}_{}\end{array}& {\hat{k}}_{}\\ \begin{array}{cc}\begin{array}{c}{\mathrm{一个}}_1\\ b_1\end{array}& \begin{array}{c}{\mathrm{一个}}_2\\ b_2\end{array}\end{array}& \begin{array}{c}{\mathrm{一个}}_{3.}\\ b_{3.}\end{array}\end{array}\right|\\ \\ =({\mathrm{一个}}_2{b}_{3.}-{\mathrm{一个}}_{3.}{b}_2)\widehat{我}+({\mathrm{一个}}_{3.}{b}_1-{\mathrm{一个}}_1{b}_{3.})\hat{j}+({\mathrm{一个}}_1{b}_2-{\mathrm{一个}}_2{b}_1)\hat{k}。\end{array}$$

$$\Vert \mathrm{一个}\times B\Vert =\Vert \mathrm{一个}\Vert \Vert B\Vert 罪\alpha 。$$