# What is the cross product of two vectors?

The cross product is not commutative, so $\vec{u} \times \vec{v} \ne \vec{v} \times \vec{u}$. If we are given 2 vectors: $\vec{u} = \left\{{u}_{1} , {u}_{2} , {u}_{3}\right\}$ and $\vec{v} = \left\{{v}_{1} , {v}_{2} , {v}_{3}\right\}$, then the formula is:
$\vec{u} \times \vec{v} = \left\{{u}_{2} \cdot {v}_{3} - {u}_{3} \cdot {v}_{2} , {u}_{3} \cdot {v}_{1} - {u}_{1} \cdot {v}_{3} , {u}_{1} \cdot {v}_{2} - {u}_{2} \cdot {v}_{1}\right\}$