Last updated Jun 30, 2026

Similarity & Vector Search

Definition: Once text is embedded into vectors, you measure how related two pieces of text are by how close their vectors are. The most common measure is cosine similarity, which ranges from 0 (unrelated) to 1 (identical direction).

The intuition

Think of each vector as an arrow. If two arrows point the same way, the texts mean similar things (similarity near 1). If they point in different directions, they are unrelated (near 0).

Run it yourself

The demo computes cosine similarity between a query vector and two document vectors. Whichever scores higher is the better match — this is the heart of "vector search".

This is exactly what a vector database does, just across millions of vectors and very fast.

💡 Key point: retrieval in RAG = embed the question, then find the document chunks with the highest similarity.

Try it Yourself

import math

def cosine(a, b):
    dot = sum(x * y for x, y in zip(a, b))
    na = math.sqrt(sum(x * x for x in a)) or 1
    nb = math.sqrt(sum(y * y for y in b)) or 1
    return dot / (na * nb)

query     = [1, 0, 1, 0]
doc_about_query   = [1, 0, 2, 1]   # shares words with the query
doc_unrelated     = [0, 3, 0, 0]   # different topic

print("Query vs related doc:  ", round(cosine(query, doc_about_query), 3))
print("Query vs unrelated doc:", round(cosine(query, doc_unrelated), 3))

Output

◀ Embeddings Explained Chunking Your Documents ▶