Answer
$\vec v_1=\frac{14}{5}i+\frac{7}{5}j, \vec v_2=\frac{1}{5}i-\frac{2}{5}j$
Work Step by Step
1. Let $\vec v_1=ai+bj, \vec v_2=ci+dj$, we have $a+c=3, b+d=1$
2. With $v_1\parallel w$, we have $\frac{b}{a}=\frac{-1}{-2}$, thus $a=2b$
3. With $v_2\perp w$, we have $c(-2)+d(-1)=0$, thus $2c=-d$
4. Combine the above results, we have $4b-d=6$ and $b+d=1$, thus $b=\frac{7}{5}$ and $d=-\frac{2}{5}$
5. Thus the two vectors are $\vec v_1=\frac{14}{5}i+\frac{7}{5}j, \vec v_2=\frac{1}{5}i-\frac{2}{5}j$
