In this paper, at some point the author is making a Fourier transform. This Fourier transform generates two spaces, one from which we may extract a position vector $\textbf{r}$ with cartesian coordinates $x$, $y$ and $z$ as its elements, and a reciprocal space from which we may extract a wavenumber vector $\textbf{q}$ with $q_x$, $q_y$ and $q_z$ as its elements. He then calculates the dot product $\textbf{q} \cdot \textbf{r}$ and interprets it as an angle (as he is putting it into a $\cos$ function, ie $\cos(\textbf{q} \cdot \textbf{r}$)).
Why can this dot product be interpreted as an angle? Is there any Fourier transform formula which directly connects $\textbf{q}$ and $\textbf{r}$ and involves such a dot product? I don't know which keywords to put in google to find a formula table which could then point me to a demonstration.