免费叉积计算器
计算两个三维向量的叉积(外积/向量积)。
Cx
-3.0000
公式
## 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
计算示例
Cross product of (2,3,4) and (5,6,7).
- 01x: 3×7 - 4×6 = 21 - 24 = -3
- 02y: 4×5 - 2×7 = 20 - 14 = 6
- 03z: 2×6 - 3×5 = 12 - 15 = -3
- 04A × B = (-3, 6, -3)
- 05|A × B| = √(9+36+9) = √54 ≈ 7.3485
常见问题
What is the cross product?
The cross product of two 3D vectors produces a vector perpendicular to both inputs. Its magnitude equals the area of the parallelogram formed by the two vectors.
Does the cross product work in 2D?
The cross product is only defined for 3D vectors. In 2D, you can treat vectors as 3D with z=0, and the result will point entirely in the z direction.
What does the magnitude represent?
The magnitude of A × B equals |A|×|B|×sin(theta), which is the area of the parallelogram spanned by the two vectors.
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