Spherical coordinates vectors

Question

I understand that in cartesian coordinates each unit vector has direction that it points in.However what would be the analogue for spherical coordinates?while ${\displaystyle \mathbf {\hat {r}}}$ points in the direction of radial distance.What directions do the ${\displaystyle \mathbf {\hat {\theta}}}$ and ${\displaystyle \mathbf {\hat {\phi}}}$ vectors point in?Can we treat them as position vectors and how do we determine all three are perpendicular to each other?Can we cross or dot them with cartesian vectors?Thanks in advance!