I have to say, neither of those answers are very satisfying. Neither is wrong but I don't come away with a clear explanation for why cosine similarity is the obvious metric to use.
Additionally, the scale of q (the query) is constant across any given search, so might as well normalize q; the results won't change.
Then the only question is whether the scale of v matters... It, again, doesn't tell us anything about the relationship between q and v. So, might as well normalize... And then we are just doing cosine similarity.