# Vector dot

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

Compute the dot (scalar) product of two equal-length finite-number vectors.

**Use when you need to: vector dot product · scalar product of two vectors · inner product.**

## Supported

- vector dot product
- scalar product of two vectors
- inner product

## Not supported

- vectors of different lengths
- complex-valued inner product
- arbitrary-precision arithmetic

## Behavior

- Inputs a and b are arrays of finite JSON numbers with the same length, from 1 to 64 entries.
- Each entry magnitude is bounded to at most 1000000 in absolute value.
- The result is the left-to-right IEEE-754 double-precision accumulation of a[i] * b[i] for every index.
- A result of -0 is normalized to 0.

## Input

- `a` (array of number, required): min items 1; max items 64
- `b` (array of number, required): min items 1; max items 64

## Output

- `result` (number, required)

## Limits

- max dim: 64
- max abs value: 1000000

## Example

Request input:

```json
{
  "a": [
    1,
    2,
    3
  ],
  "b": [
    4,
    5,
    6
  ]
}
```

Response:

```json
{
  "result": {
    "result": 32
  }
}
```

## How to call it

### MCP

Connect `https://computefirst.net/mcp` ([setup](/docs#connect)), then call `execute` with:

```json
{
  "id": "vector-dot",
  "version": "1.0.0",
  "input": {
    "a": [
      1,
      2,
      3
    ],
    "b": [
      4,
      5,
      6
    ]
  }
}
```

### HTTP (no key)

```sh
curl -X POST https://computefirst.net/v1/tools/vector-dot/versions/1.0.0/execute \
  -H "Content-Type: application/json" \
  -d '{"a":[1,2,3],"b":[4,5,6]}'
```

The machine-readable contract is at [/v1/tools/vector-dot/versions/1.0.0](/v1/tools/vector-dot/versions/1.0.0).

### CLI

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

Get the client at [/clients/cli/](/clients/cli/).

## Related tools

- [Vector outer product](/tools/vector-outer-product): Compute the outer product of two finite-number vectors, producing a matrix.
- [Vector add](/tools/vector-add): Add two equal-length finite-number vectors elementwise.
- [Vector lerp](/tools/vector-lerp): Linearly interpolate (or extrapolate) between two equal-length finite-number vectors.
- [Matrix multiply](/tools/matrix-multiply): Multiply an MxK finite-number matrix by a KxN finite-number matrix, producing an MxN matrix.
- [Vector angle](/tools/vector-angle): Compute the angle in radians between two equal-length finite-number vectors.
- [Vector approx equal](/tools/vector-approx-equal): Compare two equal-length finite-number vectors for approximate equality within an absolute tolerance.