Base unit (measurement) aspects of the world, such as time, distance, velocity, mass, temperature, energy, and weight, and "units" are used to describe their magnitude or quantity. Many of these quantities are related to each other by various physical laws, and as a result the units of a quantities can be generally be expressed as a product of powers of other units; for example, momentum is mass multiplied by velocity, while velocity is measured in distance divided by time. These relationships are discussed in dimensional analysis. Those that can be expressed in this fashion in terms of the base units are called .
Velocity-addition formula for the perpendicular and parallel components can be cast in vector form as follows, a trick which also works for Lorentz transformations of other 3d physical quantities originally in set up standard configuration. Introduce the velocity vector in the unprimed frame and in the primed frame, and split them into components parallel ( ∥ ) and perpendicular (⊥) to the relative velocity vector (see hide box below) thus then with the usual Cartesian unit basis vectors , set the velocity in the unprimed frame to be which gives, using the results for the standard configuration, where · is the dot