Does the dot product angle formula work for $\Bbb{R}^n$? Whenever I have seen this formula discussed 
\begin{equation}
\textbf{A} \cdot \textbf{B} = \|\textbf{A} \| \|\textbf{B} \| \cos\theta
\end{equation}
I have always seen it using vectors in $\Bbb{R}^2$. 
I was wondering if this property works if $\dim \textbf{A}= \dim \textbf{B} = n$. I feel like it wouldn't because for spherical coordinates we need more than one angle. We use $\phi$ and $\theta$. But I have no idea. Maybe I am confusing the meaning of $\theta$ in the dot product angle formula. It isn't a dimension right? 
My Question: 
Does the dot product angle formula apply to $\Bbb{R}^n$?

Yes. It does. The inner product is defined in n space in linear algebra. https://www.princeton.edu/~achaney/tmve/wiki100k/docs/Euclidean_space.html. You should also read the wikipedia article on inner product. 
