I am trying to express the vector field $A = xz\hat{x} + y\hat{y}$ in cylindrical polar coordinates.
The coefficient of the $\hat{e}_\phi$ vector is $A \cdot \hat{e}_\phi$. I am now trying to evaluate what $\hat{x}\cdot\hat{e}_\phi$ and $\hat{y}\cdot\hat{e}_\phi$ are. Can somebody help me first visualize what $\hat{e}_\phi$ looks like (for example what direction is this unit vector pointing in) and also evaluate the aforementioned dot products.