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 .
Cross product a and b provides an alternative definition of the cross product. The relation: can be compared with another relation involving the right-hand side, namely Lagrange's identity expressed as: where a and b may be "n"-dimensional vectors. This also shows that the Riemannian volume form for surfaces is exactly the surface element from vector calculus. In the case where , combining these two equations results in the expression for the magnitude of the cross product in terms of its components: The same result is found directly using the components of the cross product found from: In R, Lagrange's equation is a