Elixir Circle Collision

defmodule PGS.Circle do
    def new(pos, rad) do
        %{:position=>pos,:radius=>rad}
    end
end

defmodule PGS.Vector do
    def zero() do
        new(0, 0, 0)
    end

    def new(a, b, c) do
        %{:x => a, :y => b, :z => c}
    end

    def add(v1, v2) do
        %{:x => v1.x + v2.x, :y => v1.y + v2.y, :z => v1.z + v2.z}
    end

    def sub(v1, v2) do
        %{:x => v1.x - v2.x, :y => v1.y - v2.y, :z => v1.z - v2.z}
    end

    def scale(v, s) do
        %{:x => v.x * s, :y => v.y * s, :z => v.z * s}
    end

    def dot(v1, v2) do
        v1.x * v2.x + v1.y * v2.y + v1.z * v2.z
    end

    def distance(v1, v2) do
        sub(v1, v2) |> PGS.Vector.len
    end

    def normalize(v) do
        m = len(v)
        if m == 0 do
            v
        else
            %{:x => v.x / m, :y => v.y / m, :z => v.z / m}
        end
    end

    def len(v) do
        Sys.Math.sqrt(v.x * v.x + v.y * v.y + v.z * v.z)
    end
end