Answer
The angle between the directions of $r$ and $F$ is $~~90^{\circ}$
Work Step by Step
We can find the angle $\phi$ between the directions of $r$ and $F$:
$\tau = r ~F~sin~\phi = 12~N\cdot m$
$(3~m)(4~N)~sin~\phi = 12~N\cdot m$
$(12~N\cdot m)~sin~\phi = 12~N\cdot m$
$sin~\phi = 1$
$\phi = 90^{\circ}$
The angle between the directions of $r$ and $F$ is $~~90^{\circ}$.
