Description
Determine handedness of an explicit ordered three-vector basis from its scalar triple product, with exact zero treated as degenerate and no orthogonality claim.
A vector is an ordered set of components in a chosen basis. Its norm measures magnitude, while dot products, projections, and coordinate transformations describe different relationships. Component order, angle units, normalization, and numerical tolerances determine the meaning of a computed result.
Determine handedness of an explicit ordered three-vector basis from its scalar triple product, with exact zero treated as degenerate and no orthogonality claim.
When to use this tool
Use Vector: Vector Three Component Handedness Sign when you need the particular coordinate operation, derivative, residual, or domain check under a known basis convention.
How to use the tool and how it works
- Enter first, second, third. Keep parallel arrays aligned. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read result. Expand result to inspect the returned fields.
Require three three-component vectors. Calculate the scalar triple product determinant and label handedness right for positive, left for negative, and degenerate for exact zero, returning fields inside result.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| first | First | Required. Array of Finite number.. |
| second | Second | Required. Array of Finite number.. |
| third | Third | Required. Array of Finite number.. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| result | Result | Required. Object. |
{
"input": {
"first": [
1,
0,
0
],
"second": [
0,
1,
0
],
"third": [
0,
0,
1
]
},
"output": {
"result": {
"scalarTripleProduct": 1,
"handedness": "right"
}
}
}Limitations and assumptions
- No tolerance or orthonormality check is applied. Near-degenerate determinants can be sensitive to rounding, and the labels assume the supplied vector order defines the basis.
- Outputs are nested inside result. The field tables state structural bounds; the mechanics also specify cross-field constraints. Malformed inputs and unsupported domains cause errors. A successful false flag, empty branch value, or zero placeholder has the meaning stated above and is distinct from an input error.
- Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Signed zero is exported as zero.
Alternative or Complementary methods
Choose a complete vector or matrix operation when a single component or residual is insufficient. For sensitive near-zero or near-singular cases, inspect numerical conditioning and use an appropriate precision and tolerance.
References
Similar or alternative tools
- Vector Reflection Axis Component Sign
Preserve the supplied parallel scalar and negate perpendicular.
- Basis Vector Determinant Sign
Inspect floating-point orientation of a supplied 3D basis after row scaling; no exact-predicate guarantee.