Scalar product measures alignment of vectors. Perpendicular vectors have dot product = 0.
Physics — Work done: W = F · d = |F||d|cos(θ).
Machine learning — Cosine similarity for document comparison.
Computer graphics — Lighting calculations (Lambert's law).
Recommendation systems — User-item similarity.
Signal processing — Correlation between signals.
NLP — Word embeddings similarity.
Robotics — Force projection calculations.
Game physics — Collision response calculations.
Navigation — GPS position fixing.
Finance — Portfolio beta calculation.
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