Answer
the vectors $u$ and $v$ verify the triangle inequality.
Work Step by Step
Given the vectors ${u}=(1,-1,0), {v}=(0,1,2)$, then their lengths can be calculated as follows
$$\|{u}\|=\sqrt{1+1+0}=\sqrt{2}, \quad \|{v}\|=\sqrt{0+1+4}=\sqrt{5}.$$
Also,
$$\|{u+v}\|=(1,0,2)=\sqrt{1+0+4}=\sqrt{5}.$$
One can see that,
$$\|{u}+{v}\| \leq\|{u}\|+\|{v}\|.$$
Hence, the vectors $u$ and $v$ satisfy the triangle inequality.
the vectors $u$ and $v$ verify the triangle inequality.