Inner product spaces
Lesson 8 of 10
Dot products and norms
Objective. Compute dot products, lengths and the angle between vectors.
The key idea
u · v = Σ uᵢvᵢ, the norm is √(v · v), and cos θ = (u · v)/(|u||v|).
Worked example
Find (1, 2, 2) · (2, 0, 1) and the length of (1, 2, 2).
- 1Dot product: 2 + 0 + 2 = 4.
- 2Norm: √(1 + 4 + 4) = √9.
Answer: Dot product 4, length 3
Practice
Each question comes with a picture and a listen button. Try it first, then reveal the answer.
Common mistake. Forgetting the square root when computing a norm.
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