# Cross Product

 $\b{a}{\times}\b{b}=\left|\begin{matrix}\b{i}&\b{j}&\b{k}\\a_1&a_2&a_3\\b_1&b_2&b_3\end{matrix}\right|=\b{i}(a_2b_3-a_3b_2)-\b{j}(a_1b_3-a_3b_1)+\b{k}(a_1b_2-a_2b_1)=\left[\begin{matrix}a_2b_3-a_3b_2\\-(a_1b_3-a_3b_1)\\a_1b_2-a_2b_1\end{matrix}\right]$
where a is the vector $\left[\begin{matrix}a_1\\a_2\\a_3\end{matrix}\right]$ , b is the vector $\left[\begin{matrix}b_1\\b_2\\b_3\end{matrix}\right]$ and i, j and k are unit vectors.