How to Calculate Vector Dot Product
What is Vector Dot Product?
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.
Step-by-Step Guide
- 1A·B = a₁b₁ + a₂b₂ + a₃b₃ (component form)
- 2cos(θ) = A·B / (|A||B|)
- 3|A| = √(a₁² + a₂² + a₃²)
Worked Examples
Input
A=[1,2,3] · B=[4,5,6]
Result
A·B = 4+10+18 = 32 · θ = 12.9°
Small angle = similar direction