Description
Differentiate first cross second with respect to one coordinate of the first vector, holding the second fixed.
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.
Differentiate first cross second with respect to one coordinate of the first vector, holding the second fixed.
When to use this tool
Use Vector Cross Product One Input Coordinate Derivative 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 second, 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 derivative. Use the output convention below.
Require second to have three components and coordinate from zero through two. Return the derivative of first cross second with respect to that selected first-vector component, giving (0,-z,y), (z,0,-x), or (-y,x,0).1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| second | Second | Required. Array of Finite number.; maximum items 256. |
| coordinate | Zero-based component of the first cross-product input to differentiate with respect to. | Required. Safe integer; minimum 0; maximum 2. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| derivative | Derivative | Required. Array of Finite number.; maximum items 256. |
{
"input": {
"second": [
2,
3,
4
],
"coordinate": 0
},
"output": {
"derivative": [
0,
-4,
3
]
}
}Limitations and assumptions
- The second vector is held fixed and no first-vector value is needed. This derivative order matters; differentiating second cross first would reverse the sign.
- 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 Normalized Area Term
Return sine=crossMagnitude/(firstNorm*secondNorm), requiring positive norms and crossMagnitude within zero and their product.
- Vector Normalization Coordinate Derivative
Calculate one Jacobian entry of vector normalization with respect to an input coordinate.