Answer
See solution
Work Step by Step
Let us suppose $c\vec{u}=\vec{0}$. Then, $c\vec{u}+c\vec{u}=\vec{0}+\vec{0}=\vec{0}$, which means $c(\vec{u}+\vec{u})=\vec{0}=c\vec{u}$ using axiom 7.
Then, $\vec{u}+\vec{u}=2\vec{u}=\vec{u}$, which can only be true if $\vec{u}$ is the zero vector