\[\mathbf{a}\times\mathbf{b}=\begin{vmatrix}\mathbf{i}&\mathbf{j}&\mathbf{k}\\
a_{1}&a_{2}&a_{3}\\
b_{1}&b_{2}&b_{3}\end{vmatrix}\\
=(a_{2}b_{3}-a_{3}b_{2})\mathbf{i}+(a_{3}b_{1}-a_{1}b_{3})\mathbf{j}+(a_{1}b_{%
2}-a_{2}b_{1})\mathbf{k}\\
=\left\|{\mathbf{a}}\right\|\left\|{\mathbf{b}}\right\|(\sin\theta)\mathbf{n},\]