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[<Struct>]
type Vector =
    { X: float; Y: float; Z: float }
    static member (*) (k, v: Vector) = { X = k * v.X; Y = k * v.Y; Z = k * v.Z }
    static member (-) (v1: Vector, v2: Vector) = { X = v1.X - v2.X; Y = v1.Y - v2.Y; Z = v1.Z - v2.Z }
    static member (+) (v1: Vector, v2: Vector) = { X = v1.X + v2.X; Y = v1.Y + v2.Y; Z = v1.Z + v2.Z }
    static member Dot (v1: Vector, v2: Vector) = v1.X * v2.X + v1.Y * v2.Y + v1.Z * v2.Z
    static member Mag (v: Vector) = sqrt (v.X * v.X + v.Y * v.Y + v.Z * v.Z)
    static member Norm (v: Vector) =
        let mag = Vector.Mag v
        let div = if mag = 0.0 then infinity else 1.0/mag
        div * v
    static member Cross (v1: Vector, v2: Vector) =
        { X = v1.Y * v2.Z - v1.Z * v2.Y
        ; Y = v1.Z * v2.X - v1.X * v2.Z
        ; Z = v1.X * v2.Y - v1.Y * v2.X }