Answer
satisfy the triangle inequality.
Work Step by Step
\noindent \textbf{(57)}
Given the vectors ${u}=(4,0), {v}=(1,1)$, then their lengths can be calculated as follows
$$\|{u}\|=\sqrt{16+0}=4, \quad \|{v}\|=\sqrt{1+1}=\sqrt{2}.$$
Also,
$$|{u+v}\|=(5,1)=\sqrt{25+1}=\sqrt{26}.$$
One can see that,
$$\|{u}+{v}\| \leq\|{u}\|+\|{v}\|.$$
Hence, the vectors $u$ and $v$ satisfy the triangle inequality.