What does it say about two curves $\vec x (t)$ and $\vec y (t)$ in $\mathbb{R}^n$ if $$|| \vec x(t) \cdot \vec y(t) || \leq || \vec x(t) \odot \vec y(t) ||?$$
That is, what are some necessary and non-trivial conditions on $\vec x(t)$ and $\vec y(t)$ in order for the equality to be met?
See my old post https://stats.stackexchange.com/a/533578/69508 for more information on the distinction between these operations.