Answer
$\frac{3\sqrt 2}{2}i+\frac{3\sqrt 2}{2}j$ or $-\frac{3\sqrt 2}{2}i-\frac{3\sqrt 2}{2}j$
Work Step by Step
1. Let $\vec v=ai+bj$, we have $a=b$, thus $\vec v=bi+bj$
2. Use its magnitude, we have $\sqrt {b^2+b^2}=3$, thus $2b^2=9$ and $b=\pm\frac{3\sqrt 2}{2}$
3. Thus we have he vector(s) $\vec v=\frac{3\sqrt 2}{2}i+\frac{3\sqrt 2}{2}j$ or $\vec v=-\frac{3\sqrt 2}{2}i-\frac{3\sqrt 2}{2}j$
