Vector Product Calculator
Calculate the cross product (vector product) of two 3D vectors. Get the resulting vector, magnitude, and step-by-step explanation.
Published by:
isCalculator Editorial Team
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How to use this tool?
This calculator computes the cross product of two 3D vectors (A × B). Follow these steps:
- Enter Vector A — Fill in the Ax, Ay, and Az fields with numeric values (e.g., 1, 2, 3).
- Enter Vector B — Fill in the Bx, By, and Bz fields with numeric values (e.g., 4, 5, 6).
- Click "Calculate Cross Product" — The result vector (Cx, Cy, Cz) and its magnitude will appear below.
- Review the steps — A step-by-step breakdown shows the formula and intermediate calculations.
Note: All values are treated as real numbers (decimals allowed). No specific units are required — just enter the numeric components of your vectors.
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Frequently Asked Questions
The vector product (cross product) of two vectors A and B is a vector perpendicular to both A and B, with magnitude equal to the area of the parallelogram formed by A and B.
Given A = (Ax, Ay, Az) and B = (Bx, By, Bz), the cross product C = A × B = (Ay*Bz - Az*By, Az*Bx - Ax*Bz, Ax*By - Ay*Bx).
The magnitude |A × B| equals |A||B|sin(θ), where θ is the angle between A and B. It represents the area of the parallelogram spanned by the vectors.
