## Calculus (3rd Edition)

If $v$ is orthogonal to $u$ and $w$, then we have $$v\cdot u=0, \quad v\cdot w=0.$$ Now, $v\cdot (u+w)=v\cdot u+v\cdot w=0$, which means that $v$ is orthogonal to $u+w$. Hence, we use the distributive property.