Thank you! So a vector field can be defined as either $$\vec A(r, \theta, \phi) = \vec r = r \hat r$$ or $$\vec A(r, \theta, \phi) = A_r(r, \theta, \phi) \hat r + A_{\theta}(r, \theta, \phi) \hat \theta + A_{\phi}(r, \theta, \phi) \hat \phi $$. Is that right?
Also then, from my understanding...