Interactive 2D Dot Product Visualization
Explore how the dot product changes as you modify the second vector's angle and magnitude. The fixed vector is v₁ = (2, 1).
Key Insights:
- Maximum dot product: When v₂ aligns with v₁ (same direction)
- Minimum dot product: When v₂ points opposite to v₁
- Zero dot product: When v₂ is perpendicular to v₁
- Formula: v₁ · v₂ = |v₁| × |v₂| × cos(θ)