I know the Surface area element for polar co-ordinates is:
dA = r dr d(theta/phi)
whereas... what is the area vector? I know the area vector is perpendicular to the to the surface plane but between x, y, r and theta/phi
which vector matches that description? I assumed the position vector/radial vector as being the "direction" for the area vector.. but i have nowhere to confirm this.
Polar coordinates consist of three "directions": $r,\varphi, z$ as opposed to spheric coordinates, which are two angles and one radius, $r,\varphi,\theta$. So your Area vector is as you said perpendicular to the area, so you have $$d \vec{A}=d A \cdot \vec{e}_z=r\cdot dr \thinspace d\varphi\cdot \vec{e}_z$$