I asked it some time ago: https://cs.stackexchange.com/questions/147713/why-word-embed...
There is other aspect: if all vectors are normalized then cosine distance is just dot product. It is faster to calculate than euclidean distance.
There is other aspect: if all vectors are normalized then cosine distance is just dot product. It is faster to calculate than euclidean distance.
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.