The angle between vectors A and B: cos(θ) = (A·B)/(|A||B|). θ = 0°: parallel (same direction). θ = 90°: perpendicular. θ = 180°: antiparallel. Cosine similarity = cos(θ), ranging from −1 to 1. In ML, high cosine similarity means similar directions.
How to Use
Enter two vectors:
- 2D: (x, y) components
- 3D: (x, y, z) components
- Result: Angle and relationship
Special Cases
- θ = 0°: parallel, same direction
- θ = 90°: perpendicular (A·B = 0)
- θ = 180°: antiparallel
- 0° < θ < 90°: acute
Cosine Similarity
Used in ML and NLP to measure text/document similarity. Range [−1, 1]. 1 = identical direction, 0 = orthogonal, −1 = opposite.
Step-by-Step Instructions
- 1Enter vector A components.
- 2Enter vector B components.
- 3Toggle 2D/3D.
- 4View the angle.
- 5Check relationship.