如何计算Vector Dot Product

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The dot product A·B = |A||B|cos(θ) produces a scalar measuring how much two vectors point in the same direction. A·B=0 means they are perpendicular. Fundamental in physics, machine learning, and computer graphics.

分步指南

1. 1A·B = a₁b₁ + a₂b₂ + a₃b₃ (component form)
2. 2cos(θ) = A·B / (|A||B|)
3. 3|A| = √(a₁² + a₂² + a₃²)

例题解析