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