Answer
$ \frac{8\sqrt 5}{5}i+\frac{4\sqrt 5}{5}j$ or $ -\frac{8\sqrt 5}{5}i-\frac{4\sqrt 5}{5}j$
Work Step by Step
1. Let $\vec v=ai+bj$, we have $a=2b$, thus $\vec v=2bi+bj$
2. Use its magnitude, we have $\sqrt {(2b)^2+b^2}=4$, thus $5b^2=16$ and $b=\pm\frac{4\sqrt 5}{5}$
3. Thus we have he vector(s) $\vec v=\frac{8\sqrt 5}{5}i+\frac{4\sqrt 5}{5}j$ or $\vec v=-\frac{8\sqrt 5}{5}i-\frac{4\sqrt 5}{5}j$
