{\displaystyle |\mathbf {a} \times \mathbf {b} |^{2}=\!\!\sum _{1\leqslant i<j\leqslant 3}\!\!(a_{i}b_{j}-a_{j}b_{i})^{2}=(a_{1}b_{2}-b_{1}a_{2})^{2}+(a_{2}b_{3}-a_{3}b_{2})^{2}+(a_{3}b_{1}-a_{1}b_{3})^{2}.}