Cross product

$a\times b:=\left|\begin{array}{ccc}{e}_1& e_2& e_3\\ a_1& a_2& a_3\\ b_1& b_2& b_3\end{array}\right|$ , where

• $e_i$ is the $i$th axis
• $a={\sum }_i{e}_i{a}_i\in {\mathbb{R}}^3$
• $b={\sum }_i{e}_i{b}_i\in {\mathbb{R}}^3$