How does the Vector Cross Product work?

A×B = [a₂b₃−a₃b₂, a₃b₁−a₁b₃, a₁b₂−a₂b₁] Then: Magnitude: |A×B| = |A||B|sin(θ) Then: A×B = −(B×A) (anti-commutative).

Can you give an example of how to use the Vector Cross Product?

Example: Input A=[1,0,0] · B=[0,1,0] gives a result of A×B = [0,0,1] (unit z-vector) (x̂ × ŷ = ẑ by right-hand rule).

Is the Vector Cross Product free to use?

Yes — completely free with no registration, download, or subscription required. All calculations happen instantly in your browser.

How accurate is the Vector Cross Product?

Our Vector Cross Product uses verified mathematical formulas and is accurate to multiple decimal places. Results are calculated in real-time using the same methods used by professionals.

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Vector Cross Product

📐Vector Cross Product (3D)

Vector A (3 values)

Vector B (3 values)

The cross product A×B of two 3D vectors produces a new vector perpendicular to both. Its magnitude equals the area of the parallelogram spanned by the two vectors. Direction follows the right-hand rule.

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Did You Know?

The cross product only exists in 3D (and 7D) — a curious mathematical fact with deep connections to the structure of division algebras.

References

›Cross product — Wikipedia

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Vector Cross Product

📐Vector Cross Product (3D)

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📐Vector Cross Product (3D)