curl --request POST \
  --url https://api.iotools.cloud/v1/tool/cross-product-calculator \
  --header 'Authorization: Bearer <token>' \
  --header 'Content-Type: application/json' \
  --data '
{
  "ax": "1",
  "ay": "0",
  "az": "0",
  "bx": "0",
  "by": "1",
  "bz": "0"
}
'

{
  "tool": "cross-product-calculator",
  "tool_version": "1.0.2",
  "outputs": {
    "results": [
      {
        "metric": "Vector a",
        "value": "(1, 0, 0)"
      },
      {
        "metric": "Vector b",
        "value": "(0, 1, 0)"
      },
      {
        "metric": "Cross Product a × b",
        "value": "(0, 0, 1)"
      },
      {
        "metric": "Unit Cross Product",
        "value": "(0, 0, 1)"
      },
      {
        "metric": "|a| (magnitude of a)",
        "value": "1"
      },
      {
        "metric": "|b| (magnitude of b)",
        "value": "1"
      },
      {
        "metric": "|a × b| (magnitude of cross product)",
        "value": "1"
      },
      {
        "metric": "Parallelogram Area (spanned by a, b)",
        "value": "1"
      },
      {
        "metric": "Triangle Area (half the parallelogram)",
        "value": "0.5"
      },
      {
        "metric": "Dot Product a · b",
        "value": "0"
      },
      {
        "metric": "Angle Between a and b",
        "value": "90°"
      },
      {
        "metric": "Are a and b parallel?",
        "value": "No"
      },
      {
        "metric": "Perpendicularity Check",
        "value": "a · (a×b) = 0, b · (a×b) = 0 (both ≈ 0 confirms a×b is perpendicular to both)"
      }
    ]
  },
  "credits_used": 5,
  "credits_remaining": null
}