# How can a generalised force be dependent on an angle i.e. not a vector?

I'm currently working through an example question in Patrick Hamill's 'A Student's Guide to Hamiltonians and Lagrangians'. The question I'm having conceptual difficulty with is:

A particle is acted upon with components $F_x$ and $F_y$. Determine the generalized forces, $Q_i$, in polar coordinates.

It's simple to find the generalised force dependence on $r$: ($Q_r = F_x\cos(\theta) + F_y\sin(\theta)$) however I can't seem to get my head around the answer for the dependence on $\theta$, (which is $-F_x r\sin(\theta) + F_y r\cos(\theta)$).

I think that the difficulty I'm having stems from $\theta$ looking a lot like a vector here in component form. As far as I am aware, angles are never vectors.

$\theta$ in this case is a coordinate, i.e. part of the description of a point. The vector associated to that coordinate could be called $\hat{e}_\theta$, and point in the direction, in which $\theta$ changes. So, in polar coordinates, the force depends on the position at which it is evaluated.