Cross Product Calculator — Formula
## Cross Product
### Formula
**A × B = (a₂b₃ - a₃b₂, a₃b₁ - a₁b₃, a₁b₂ - a₂b₁)**
### Properties
- The result is **perpendicular** to both input vectors
- **|A × B| = |A| × |B| × sin(theta)** (area of parallelogram)
- A × B = -(B × A) (anticommutative)
- If A × B = (0,0,0), the vectors are parallel
### Formula
**A × B = (a₂b₃ - a₃b₂, a₃b₁ - a₁b₃, a₁b₂ - a₂b₁)**
### Properties
- The result is **perpendicular** to both input vectors
- **|A × B| = |A| × |B| × sin(theta)** (area of parallelogram)
- A × B = -(B × A) (anticommutative)
- If A × B = (0,0,0), the vectors are parallel
Esempio Risolto
Cross product of (2,3,4) and (5,6,7).
- x: 3×7 - 4×6 = 21 - 24 = -3
- y: 4×5 - 2×7 = 20 - 14 = 6
- z: 2×6 - 3×5 = 12 - 15 = -3
- A × B = (-3, 6, -3)
- |A × B| = √(9+36+9) = √54 ≈ 7.3485