The dot product, and why similarity is just an angle

After this lesson you can: Explain why two similar things have a large dot product.

First: Vectors, and what they actually represent

Watch

• Cosine Similarity, Clearly Explained!!! - StatQuest with Josh Starmer, 10 min. Directly targets similarity as vector angle, with beginner-friendly framing from a trusted statistics teaching channel.
• Dot products and duality | Chapter 9, Essence of linear algebra - 3Blue1Brown, 14 min. Builds geometric intuition for dot products, helping engineers see the formula as meaningful, not arbitrary.

Notes

A vector can represent an object as a list of numbers: features, measurements, counts, ratings, or embedding coordinates. The dot product multiplies matching coordinates and adds the results. That sounds like a mechanical formula, but geometrically it measures how much two vectors point in the same direction, especially when their lengths are controlled or normalized.

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