📐Vector Dot Product Calculator
e.g. 1, 2, 3
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.
- 1A·B = a₁b₁ + a₂b₂ + a₃b₃ (component form)
- 2cos(θ) = A·B / (|A||B|)
- 3|A| = √(a₁² + a₂² + a₃²)
A=[1,2,3] · B=[4,5,6]=A·B = 4+10+18 = 32 · θ = 12.9°Small angle = similar direction
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Fun Fact
The dot product is the foundation of cosine similarity — used by search engines and recommendation systems to compare documents represented as vectors.
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