Answer:
[tex]\large\boxed{\left<1,\ -2\right>}[/tex]
Step-by-step explanation:
[tex]\vec{v}=\left<x,\ y\right>\\\\x:\\x<0-\text{to the left}\\x>0-\text{to the right}\\\\y:\\y<0-\text{down}\\y>0-\text{up}[/tex]
[tex]\text{1 unit to the right}\to x=1\\\text{2 units down}\to y=-2\\\\\vec{v}=\left<1,\ -2\right>\\[/tex]