[frabcus]

The vectors are usually (if you use OpenAI API anyway) unit in length, and so you can imagine them on the surface of a hypersphere.

You measure the cosine distance between documents, or between search queries and documents. (Cosine is fast, there are other distance metrics).

The vector database queries will do things like given one embedding (document or query) find the nearest embeddings (documents). Or given two embeddings (e.g. a query and a context) with a weight for each one, find the ones that triangulate to being near both.