Examples
Examples
Try the starting example
- First three-dimensional real vector
- 1,0,0
- Second three-dimensional real vector
- 0,1,0
- Right-handed cross-product vector
- 0, 0, 1
- Parallelogram area
- 1
Try another scenario
- First three-dimensional real vector
- 1,0,0
- Second three-dimensional real vector
- 2,0,0
- Right-handed cross-product vector
- 0, 0, 0
- Parallelogram area
- 0
Calculation method
Calculation method
Right-handed cross-product vector
(a2b3−a3b2, a3b1−a1b3, a1b2−a2b1).
Parallelogram area
Euclidean norm of the cross product.
Symbols and units
- a
- First three-dimensional real vector
- b
- Second three-dimensional real vector
Use the units shown. A list keeps the order in which you enter its values. The symbol ^ means “raised to the power of”.
Assumptions & limits
Assumptions & limits
- Three-dimensional right-handed Euclidean coordinates only. Zero or parallel vectors yield zero area. Double-precision results are approximate. Numeric tables use 12 significant digits and display components at roundoff scale (32 machine epsilons relative to their row or relevant calculation scale) as zero; scalar diagnostics retain full precision.
Are these inputs private?
These calculations run in your browser. A shared link contains the values you choose to share. Only questions submitted to the separate AI finder are sent to OpenAI.
Further reading
OpenStax: cross product and parallelogram area ↗
Background reading; this does not imply endorsement or independent review of SumFizz.