Cross Product Calculator (A × B)
A₁ (x)
A₂ (y)
A₃ (z)
B₁ (x)
B₂ (y)
B₃ (z)
✓A × B
(-3.0000, 6.0000, -3.0000)
|A × B| (magnitude)
7.3485
The cross product of two 3D vectors produces a third vector perpendicular to both. Its magnitude equals the area of the parallelogram formed by the two vectors. It is used in physics, 3D graphics, and engineering.
- 1A × B = (AyBz−AzBy, AzBx−AxBz, AxBy−AyBx)
- 2|A × B| = |A||B|sin(θ)
- 3Result is perpendicular to both A and B
- 4Right-hand rule determines direction
A=(1,0,0), B=(0,1,0)=A×B = (0,0,1) — unit z vector
A=(1,2,3), B=(4,5,6)=(−3,6,−3)
| Property | Formula/Description |
|---|---|
| Magnitude | |A||B|sin θ |
| Direction | Perpendicular to both (right-hand) |
| Anti-commutative | A×B = −(B×A) |
| Parallel vectors | A×B = 0 when θ=0 |
| Area | |A×B| = area of parallelogram |
References
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