Cross product calculator
Calculator
The calculator needs JavaScript. The tables below give the same numbers for common cases.
How it is worked out
- A × B = (a₂b₃ − a₃b₂, a₃b₁ − a₁b₃, a₁b₂ − a₂b₁).
- The result is perpendicular to both vectors; its length is |A||B| sin θ.
| Inputs | Answer |
|---|---|
| Vector A: 2, 3, 4; Vector B: 5, 6, 7 | A × B = (-3, 6, -3), magnitude 7.3485. |
| Vector A: 1, 0, 0; Vector B: 0, 1, 0 | A × B = (0, 0, 1), magnitude 1. |
| Vector A: 3, -3, 1; Vector B: 4, 9, 2 | A × B = (-15, -2, 39), magnitude 41.833. |
How to use it
The cross product of A = (a₁, a₂, a₃) and B = (b₁, b₂, b₃) is (a₂b₃ − a₃b₂, a₃b₁ − a₁b₃, a₁b₂ − a₂b₁). It is perpendicular to both vectors, and its length is the area of the parallelogram they span. For (2, 3, 4) × (5, 6, 7) the result is (−3, 6, −3).
The dot product and the angle between the vectors are shown too.
Frequently asked questions
What is the cross product of (2,3,4) and (5,6,7)?
(−3, 6, −3).
What does the cross product give?
A vector perpendicular to both inputs.
What is the magnitude of the cross product?
The area of the parallelogram formed by the two vectors.
Method: standard arithmetic shown step by step; no outside data is used. Checked 2026-11-12.
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General information only. Results are plain arithmetic on the numbers you enter; check anything important (money, health, school work) against your own records or the official source.