## Calculus (3rd Edition)

$$\|v+w\|= \sqrt{10}.$$
Since $v=\langle -2,5\rangle$ and $w=\langle 3,-2\rangle$, then we have $$v+w=\langle -2,5 \rangle+\langle 3,-2 \rangle =\langle 1,3 \rangle.$$ Hence, the length of $v+w$ is given by $$\|v+w\|=\sqrt{1^2+3^2}=\sqrt{10}.$$