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Dot Product
★★☆☆☆Middle School
📖Definition
The sum of products of corresponding components, resulting in a scalar. Used to find angles between vectors.
📐Formulas
\vecu · \vecv = u₁v₁ + u₂v₂ + ... + uₙvₙ
Dot product definition (component)
\vecu · \vecv = |\vecu||\vecv|cosθ
Geometric definition
cosθ = \frac\vecu · \vecv|\vecu||\vecv|
Angle between vectors
✏️Examples
예제 1★★☆☆☆
Find the dot product of u = (1, 2, 3) and v = (4, 5, 6).
예제 2★★☆☆☆
Find the angle between u = (1, 0) and v = (0, 1).
⚡Applications
Physics
Work = Force · Displacement
Machine Learning
Cosine similarity
Computer Graphics
Lighting calculations
🔗Related Documents
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