Cross Product Calculator
Compute the cross product of two three-dimensional vectors.
This tool is for informational and educational purposes only. It is not a substitute for professional financial, medical, legal, or engineering advice. See Terms of Service.
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Request a ToolHow to Use the Cross Product Calculator
This tool computes the cross product of two 3D vectors.
- Enter Vector A. Type three comma-separated values (e.g. 1, 2, 3).
- Enter Vector B. Type three comma-separated values.
- View the result. The cross product vector and its magnitude update live.
About the Cross Product
The cross product of two vectors A and B produces a third vector that is perpendicular to both. Its magnitude equals the area of the parallelogram formed by A and B. The formula uses the determinant of a 3x3 matrix with unit vectors i, j, k in the first row and the components of A and B in the remaining rows. The cross product is essential in physics for torque, magnetic force, and angular momentum calculations.
Frequently Asked Questions
Is the cross product commutative?
No. A x B = -(B x A). The cross product is anti-commutative, meaning swapping the order reverses the direction.
What does the magnitude of the cross product represent?
The magnitude equals the area of the parallelogram spanned by the two input vectors.
Does the cross product work in 2D?
The standard cross product is defined only for 3D vectors. In 2D, you can treat vectors as 3D with a zero z-component to get a scalar result along the z-axis.