Dot products and similarity

A dot product combines two vectors into one number that reflects how aligned they are. In AI, it often stands in for similarity—especially after vectors are normalized.

Embeddings, attention scores, and many recommenders lean on “how close are these vectors?” Understanding the picture prevents treating cosine similarity as magic.

If two arrows point the same way, their dot product is larger (for a given length). If they point opposite ways, it shrinks or goes negative. Cosine similarity focuses on angle, not raw length.

Two playlists that share many “vibe dimensions” score as similar—even if one playlist is longer.

Write two 3-number vectors for “sports car” vs “family van.” Guess which pair of dimensions differ most.

⚠️ Myth: Highest similarity always means “same meaning.”

✓ Reality: It means close in that embedding space—which can be weird or biased.

⚠️ Myth: Longer vectors are automatically “more similar.”

✓ Reality: Length and angle are different; cosine separates them.

• 3Blue1Brown linear algebra intuition: https://www.3blue1brown.com/ ↗
• Course 04 scalars-vectors-matrices; Course 07 embeddings
• Course 09 RAG similarity search