Answer
$$\mathbf{v}= \langle 2,-1\rangle $$
Work Step by Step
$$
3 \mathbf{v}+\langle 5,20\rangle=\langle 11,17\rangle \Longrightarrow 3 \mathbf{v}=\langle 11- 5,17-20\rangle\\
\Longrightarrow \mathbf{v}=\frac{1}{3}\langle 6,-3\rangle=\langle 2,-1\rangle
$$