Vector Ops

{
  "angleDeg": 12.9331544919,
  "angleRad": 0.225726128553,
  "asOf": "2026-10-11T08:51:20.682Z",
  "cosineOfAngle": 0.974631846197,
  "cross": [
    -3,
    6
  ],
  "degraded": false,
  "difference": [
    -3,
    -3
  ],
  "disclaimer": "Screening signal computed from the named public source. Not financial, legal or investment advice; provided as is. Verify at the source before acting.",
  "distanceBetweenTips": 5.19615242271,
  "dot": 32,
  "magnitudeU": 3.74165738677,
  "magnitudeV": 8.77496438739,
  "notChecked": [
    "the cross product exists only in 3 dimensions (and 2 as a scalar z-component), so it is omitted otherwise",
    "units"
  ],
  "orthogonal": false,
  "parallel": false,
  "parallelogramArea": 7.34846922835,
  "projectionOfUOntoV": [
    1.66233766234,
    2.07792207792
  ],
  "reasons": [
    "Dot product u.v = sum of component products = |u||v|cos(angle).",
    "Cross product is perpendicular to both and its length is the parallelogram area."
  ],
  "rejectionOfUFromV": [
    -0.662337662338,
    -0.0779220779221
  ],
  "scalarProjectionOfUOntoV": 3.64673844671,
  "source": "computed locally",
  "sum": [
    5,
    7
  ],
  "summary": "u.v = 32; |u| = 3.7416574, |v| = 8.7749644; angle 12.933154 degrees; u x v = (-3, 6, -3).",
  "triangleArea": 3.67423461417,
  "unitU": [
    0.267261241912,
    0.534522483825
  ],
  "unitV": [
    0.455842305839,
    0.569802882298
  ],
  "verdict": "COMPUTED"
}

# bash or zsh: see the payment challenge. Nothing is charged.
curl -sS -g -i 'https://math-geometry.x402tookit.com/vector-ops?u=1%2C2%2C3&v=4%2C5%2C6'

# x402 v2 sends the challenge base64-encoded in the PAYMENT-REQUIRED header (v1 sends it in the body).
# To read the header:
curl -sS -g -o /dev/null -D - 'https://math-geometry.x402tookit.com/vector-ops?u=1%2C2%2C3&v=4%2C5%2C6' \
  | grep -i '^payment-required:' | cut -d' ' -f2 | tr -d '\r' | base64 --decode

// npm i @x402/fetch @x402/evm viem
import { wrapFetchWithPayment, x402Client } from "@x402/fetch";
import { registerExactEvmScheme } from "@x402/evm/exact/client";
import { privateKeyToAccount } from "viem/accounts";

// Pays at most $0.02 per call.
const client = new x402Client().setSpendControls({ maxAmountPerPayment: "$0.02" });
registerExactEvmScheme(client, { signer: privateKeyToAccount(process.env.EVM_PRIVATE_KEY) });
const pay = wrapFetchWithPayment(fetch, client);

// Not sure it's safe to pay? ToolVet checks it first for $0.005. Pay for that from a separate
// client: this one is capped at $0.02 per payment. GET https://toolvet.app/api/v1/check?url=https%3A%2F%2Fmath-geometry.x402tookit.com%2Fvector-ops
const res = await pay("https://math-geometry.x402tookit.com/vector-ops?u=1%2C2%2C3&v=4%2C5%2C6");
console.log(res.status, await res.text());

# pip install "x402[requests,evm]"
import os
from eth_account import Account
from x402 import x402ClientSync
from x402.http.clients import x402_requests
from x402.mechanisms.evm import EthAccountSigner
from x402.mechanisms.evm.exact.register import register_exact_evm_client

# Pays at most $0.02 per call.
client = x402ClientSync().set_spend_controls({"max_amount_per_payment": "$0.02"})
register_exact_evm_client(client, EthAccountSigner(Account.from_key(os.environ["EVM_PRIVATE_KEY"])))

with x402_requests(client) as session:
    res = session.get("https://math-geometry.x402tookit.com/vector-ops?u=1%2C2%2C3&v=4%2C5%2C6")
    print(res.status_code, res.text)