Description
Calculate one coordinate of a cross (b cross c) using the vector triple-product identity.
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.
Calculate one coordinate of a cross (b cross c) using the vector triple-product identity.
When to use this tool
Use Vector Triple Cross One Coordinate 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 a, b, c, coordinate. 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 value. Use the output convention below.
Require three-component a, b, and c and coordinate from zero through two. Return the selected component of a cross (b cross c) as b[coordinate]*dot(a,c)-c[coordinate]*dot(a,b).1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| a | A | Required. Array of Finite number.; maximum items 256. |
| b | B | Required. Array of Finite number.; maximum items 256. |
| c | C | Required. Array of Finite number.; maximum items 256. |
| coordinate | Coordinate | Required. Safe integer; minimum 0; maximum 2. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| value | Value | Required. Finite number. |
{
"input": {
"a": [
1,
2,
3
],
"b": [
4,
5,
6
],
"c": [
7,
8,
9
],
"coordinate": 0
},
"output": {
"value": -24
}
}Limitations and assumptions
- The order of the nested cross product matters. This computes one coordinate using a vector identity, not both cross products as full returned vectors, and no unit normalization is applied.
- 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 Cross Product One Input Coordinate Derivative
Differentiate first cross second with respect to one coordinate of the first vector, holding the second fixed.
- Vector 3d Coordinate Cyclic Permutation
Cyclically reorder three coordinates by an integer shift modulo three.