Only time and the coordinates parallel to the direction of relative motion change, while those coordinates perpendicular do not. With this in mind, split the spatial position vector r as measured in F, and r ′ as measured in F′, each into components perpendicular (⊥) and parallel (‖) to v, r = r ⊥ ⊥ + r ‖ ‖ , r ′ = r ⊥ ⊥ ′ + r ‖ ‖ ′ , then the transformations are t ′ = γ γ ( t − − r ∥ ∥ ⋅ ⋅ v c 2 ) r ‖ ‖ ′ = γ γ ( r ‖ ‖ − − v t ) r ⊥ ⊥ ′ = r ⊥ ⊥ where · is the dot product. The Lorentz factor γ retains its definition for a boost in any direction, since it depends only on the magnitude of the relative velocity. The definition β = v / c with magnitude 0 ≤ β < 1 is also used by some authors.