## Calculus 8th Edition

Consider $u=\lt 1,0,0\gt$ and $v=\lt 0,1,0\gt$ Then $|u+v|=|\lt 1,1,0\gt|=(1^{2}+1^{2})=\sqrt 2$ and $|u|+|v|=(1^{2}+0^{2}+0^{2})+(0^{2}+1^{2}+0^{2})=2$ Thus $\sqrt 2\ne 2$ Hence, the statement is false.