Find a formula $\vec{F} = \langle\ F_1(x,y),\ F_2(x,y)\ \rangle$ for the vector field in the plane with the following properties:

1. $\vec{F}$ is not defined at the origin
2. At any other point $(x,y) \ne (0,0)$ the vector field $\vec{F}$ points away from the origin with magnitude inversely proportional to the square of the distance from $(x,y)$ to the origin.
3. At the point $(1,0)$ the vector field $\vec{F}$ has magnitude $1$.

$\vec{F} =$