# Step 01 — Vectors

> You know this cold. The point of this step is to make the red→green loop
> automatic, not to teach you arithmetic. Blast through it.

## Concept

A **vector** here is nothing mystical: a pair of numbers `(x, y)`. We use the
same value to mean two different things depending on context:

- a **position** — a point in the world.
- a **displacement / velocity** — an arrow: "move this much in x, this much in
  y."

That's it. All of 2D physics is built on adding, subtracting, and scaling these
pairs.

- `add(a, b)` → `(a.x + b.x, a.y + b.y)` — apply an arrow to a point.
- `sub(a, b)` → `(a.x - b.x, a.y - b.y)` — the arrow that points _from b to a_.
- `scale(a, s)` → `(a.x * s, a.y * s)` — make an arrow longer/shorter.

> Note: we return **new** objects (pure functions) here for clarity. Your real
> engine mutates vectors in place to avoid garbage collection — that's a speed
> optimization we'll deliberately ignore until the very end.

## Task

Implement `vec`, `add`, `sub`, and `scale` in `vector.ts`.

```sh
bun test workshop/steps/01-vectors
```