Find a formula $\vec{F} = \langle\ F_1(x,y),\ F_2(x,y)\ \rangle$ for the vector field in the plane that has the properties that $\vec{F}(0,0) = \langle 0,0 \rangle$ and that at any other point $(a,b) \ne (0,0)$ the vector field $\vec{F}$ is tangent to the circle $x^2+y^2 = a^2+b^2$ and points in the counterclockwise direction with magnitude $\| \vec{F}(a,b) \| = 2 \sqrt{a^2+b^2}$.

$\vec{F} =$