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THE FEUTEX TOOLKIT

Vector Cross Product

Calculate a three-dimensional cross product and the parallelogram area spanned by two vectors.

Geometry workspace● Runs in your browser
01 Your input
02 Your result
View or copy raw result data
FormulaX = ay*bz-az*by; Y = az*bx-ax*bz; Z = ax*by-ay*bx; Parallelogram Area = hypot(ay*bz-az*by,az*bx-ax*bz,ax*by-ay*bx)
Sources and model references

Worked example

Inputs

AX
1 number
AY
0 number
AZ
0 number
BX
0 number
BY
2 number
BZ
0 number

Expected results

X
0 number
Y
0 number
Z
2 number
Parallelogram Area
2 length²

Load the example in the workspace to reproduce these results. Display rounding does not change the underlying calculation.

How to use this tool

  1. Enter the labeled inputs using consistent units.
  2. Check the stated assumptions and calculate.
  3. Review each output and compare another input scenario.

Try this example

{
  "ax": 1,
  "ay": 0,
  "az": 0,
  "bx": 0,
  "by": 2,
  "bz": 0
}

Accuracy and scope

Finite floating-point arithmetic; results can lose precision near singular or extreme inputs.

Is my data uploaded?

This tool runs locally in your browser. Input and output are not sent to a processing server. Copy or download your result before leaving the page.