import type { Vec } from "./given.ts";

/** The length (magnitude) of the arrow. */
export function length(a: Vec): number {
	return Math.sqrt(a.x * a.x + a.y * a.y);
}

/**
 * A unit-length vector pointing the same way as `a`.
 * MUST return (0, 0) when `a` is the zero vector — do not divide by zero.
 */
export function normalize(a: Vec): Vec {
	const len = length(a);
	const x = a.x === 0 ? 0 : a.x / len;
	const y = a.y === 0 ? 0 : a.y / len;

	return { x, y };
}

/** The dot product a·b. */
export function dot(a: Vec, b: Vec): number {
	return a.x * b.x + a.y * b.y;
}