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Vector Cross Product Calculator

Use this vector cross product calculator to calculate the cross product of two vectors in 3D or 2D. The calculator returns the vector components of A × B and illustrates the direction using the right-hand rule.

Cross Product of Two Vectors

Enter the components of vectors A and B. For 2D vectors, set both z-components to 0.

Vector Inputs

Use “.” as the decimal separator.

Cross Product Result

A × B = (AyBz − AzBy , AzBx − AxBz , AxBy − AyBx)

Cx =

Cy =

Cz =

Calculation Steps

Meaning of the result

Enter two vectors to calculate their cross product.

How to Calculate a Cross Product

  1. Write the components of vectors A and B.
  2. Compute AyBz − AzBy.
  3. Compute AzBx − AxBz.
  4. Compute AxBy − AyBx.
  5. The resulting vector is the cross product.

FAQ

What is the cross product formula?

A × B = (AyBz − AzBy, AzBx − AxBz, AxBy − AyBx).

What does the cross product represent?

The cross product produces a vector perpendicular to both vectors. Its magnitude equals the area of the parallelogram formed by the two vectors.

Can the cross product be calculated for 2D vectors?

Yes. Set the z-components equal to zero.

Is the cross product commutative?

No. In general, A × B = −(B × A).