Vector cross

vector-cross · version 1.0.0 · Vectors & matrices · free, no key needed

Compute the 3-dimensional cross product of two finite-number vectors.

Use when you need to: vector cross product · 3d cross product · vector product.

Supported

• vector cross product
• 3d cross product
• vector product

Not supported

• vectors of dimension other than 3
• 7-dimensional cross product
• arbitrary-precision arithmetic

Behavior

• Inputs a and b are each arrays of exactly 3 finite JSON numbers, magnitude bounded to at most 1000000.
• The result is the standard right-handed cross product: [a1*b2-a2*b1, a2*b0-a0*b2, a0*b1-a1*b0] using zero-based indices.
• Computed with IEEE-754 double-precision arithmetic; a result entry of -0 is normalized to 0.
• Only 3-dimensional vectors are supported; there is no 2D or 7D variant.

Input

• a (array of number, required): min items 3; max items 3
• b (array of number, required): min items 3; max items 3

Output

• result (array of number, required): min items 3; max items 3

Limits

• dim: 3
• max abs value: 1000000

Example

Request input:

{
  "a": [
    1,
    0,
    0
  ],
  "b": [
    0,
    1,
    0
  ]
}

Response:

{
  "result": {
    "result": [
      0,
      0,
      1
    ]
  }
}

How to call it

MCP

Connect https://computefirst.net/mcp (setup), then call execute with:

{
  "id": "vector-cross",
  "version": "1.0.0",
  "input": {
    "a": [
      1,
      0,
      0
    ],
    "b": [
      0,
      1,
      0
    ]
  }
}

HTTP (no key)

curl -X POST https://computefirst.net/v1/tools/vector-cross/versions/1.0.0/execute \
  -H "Content-Type: application/json" \
  -d '{"a":[1,0,0],"b":[0,1,0]}'

The machine-readable contract is at /v1/tools/vector-cross/versions/1.0.0.

CLI

node cli.mjs run vector-cross 1.0.0 --input input.json --base-url https://computefirst.net

Get the client at /clients/cli/.

Related tools

• Vector dot: Compute the dot (scalar) product of two equal-length finite-number vectors.
• Vector hadamard: Multiply two equal-length finite-number vectors elementwise (Hadamard product).
• Vector outer product: Compute the outer product of two finite-number vectors, producing a matrix.
• Matrix hadamard: Multiply two equal-shape finite-number matrices elementwise (Hadamard product).
• Matrix multiply: Multiply an MxK finite-number matrix by a KxN finite-number matrix, producing an MxN matrix.
• Matrix vector multiply: Multiply an MxN finite-number matrix by a length-N finite-number vector, producing a length-M vector.