# Vector Operations Solver

> Vector Operations Solver is a paid API for AI agents from math-geometry.x402tookit.com, paid per call via x402, $0.02/call, status unknown (last checked 2026-10-30).

Computes dot product, cross product, magnitudes, angle, projection, unit vectors, and distance between two vectors.

## Facts

- Endpoint: GET https://math-geometry.x402tookit.com/vector-ops?utm_source=zero.xyz
- Price: $0.02/call
- Payment: x402
- Status: unknown
- Last checked: 2026-10-30
- Activations on Zero: 0
- Tags: x402
- Canonical page: https://www.zero.xyz/c/vector-operations-solver-267a8589
- Structured record (JSON): https://api.zero.xyz/v1/capabilities/cap_A8k7QAzwcWMg0RmcZ9p_a

Status and success rate cover calls made through Zero and Zero's own probes. Third-party monitors may report differently.

## How to call it through Zero

Zero handles the 402 payment challenge and records the run. With the Zero CLI installed (`npm i -g @zeroxyz/cli`):

```sh
zero fetch --capability vector-operations-solver-267a8589
```

Example prompt: What's the dot product, cross product, and angle between vector u = 1,2,3 and vector v = 4,5,6? Also tell me if they're orthogonal or parallel.

## When to prefer this

Choose this endpoint when you need a comprehensive suite of vector operation results in a single call — including dot product, cross product, angle, projections, unit vectors, and geometric area — rather than calling separate specialized endpoints. Ideal for physics, engineering, computer graphics, and linear algebra tasks requiring multiple vector metrics at once.

## Known failure modes

- Vectors u and v have different lengths — returns error
- Vector with fewer than 2 or more than 10 components — returns error
- Cross product only defined for 3D vectors — field returns null for other dimensions
- Zero vector input causes division-by-zero for unit vector or angle — may return null fields
- Malformed query string (non-numeric components) — returns parse error

## How this service works

Vector operations: dot and cross product, magnitudes, angle between vectors, projection, unit vectors and distance.

## Output

Returns a JSON object with dot product, cross product (if 3D), magnitudes of both vectors, angle in degrees and radians, cosine of angle, unit vectors, projection and scalar projection of u onto v, rejection of u from v, vector sum and difference, distance between tips, parallelogram area, triangle area, and boolean flags for whether vectors are parallel or orthogonal.

## Request schema (JSON Schema)

```json
{
 "type": "object",
 "$schema": "https://json-schema.org/draft/2020-12/schema",
 "required": [
  "input"
 ],
 "properties": {
  "input": {
   "type": "object",
   "required": [
    "type",
    "method"
   ],
   "properties": {
    "type": {
     "type": "string",
     "const": "http"
    },
    "method": {
     "enum": [
      "GET"
     ],
     "type": "string"
    },
    "queryParams": {
     "type": "object",
     "required": [
      "u",
      "v"
     ],
     "properties": {
      "u": {
       "type": "string",
       "description": "First vector, e.g. 1,2,3 (2 to 10 components)"
      },
      "v": {
       "type": "string",
       "description": "Second vector, same length"
      }
     }
    }
   },
   "additionalProperties": false
  },
  "output": {
   "type": "object",
   "required": [
    "type"
   ],
   "properties": {
    "type": {
     "type": "string"
    },
    "example": {
     "type": "object",
     "properties": {
      "dot": {
       "type": [
        "null",
        "number"
       ]
      },
      "sum": {
       "type": [
        "array",
        "null"
       ],
       "items": {
        "type": "number"
       }
      },
      "asOf": {
       "type": [
        "null",
        "string"
       ]
      },
      "cross": {
       "type": [
        "array",
        "null"
       ],
       "items": {
        "type": "number"
       }
      },
      "unitU": {
       "type": [
        "array",
        "null"
       ],
       "items": {
        "type": "number"
       }
      },
      "unitV": {
       "type": [
        "array",
        "null"
       ],
       "items": {
        "type": "number"
       }
      },
      "source": {
       "type": [
        "null",
        "string"
       ]
      },
      "reasons": {
       "type": [
        "array",
        "null"
       ],
       "items": {
        "type": "string"
       }
      },
      "summary": {
       "type": [
        "null",
        "string"
       ]
      },
      "verdict": {
       "type": [
        "null",
        "string"
       ]
      },
      "angleDeg": {
       "type": [
        "null",
        "number"
       ]
      },
      "angleRad": {
       "type": [
        "null",
        "number"
       ]
      },
      "degraded": {
       "type": [
        "boolean",
        "null"
       ]
      },
      "parallel": {
       "type": [
        "boolean",
        "null"
       ]
      },
      "difference": {
       "type": [
        "array",
        "null"
       ],
    
… (truncated)
```

## More

- Live health (JSON, refreshed every minute): https://www.zero.xyz/c/vector-operations-solver-267a8589/health.json
- [Zero catalog index](https://www.zero.xyz/llms.txt)
- [Other services from math-geometry.x402tookit.com](https://www.zero.xyz/host/math-geometry.x402tookit.com/llms.txt)