Answer
$\vec v_1=\frac{4}{5}i-\frac{8}{5}j, \vec v_2=\frac{6}{5}i+\frac{3}{5}j$
Work Step by Step
1. Let $\vec v_1=ai+bj, \vec v_2=ci+dj$, we have $a+c=2, b+d=-1$
2. With $v_1\parallel w$, we have $\frac{b}{a}=\frac{-2}{1}$, thus $2a=-b$
3. With $v_2\perp w$, we have $c(1)+d(-2)=0$, thus $c=2d$
4. Combine the above results, we have $-b+4d=4$ and $b+d=-1$, thus $b=-\frac{8}{5}$ and $d=\frac{3}{5}$
5. Thus the two vectors are $\vec v_1=\frac{4}{5}i-\frac{8}{5}j, \vec v_2=\frac{6}{5}i+\frac{3}{5}j$
