Abstract
The use of two-dimensional vector algebra is illustrated in the mathematical treatment of hydrodynamic plane flow and horizontal atmospheric winds. These are just two possible examples of the simplification obtainable in mathematical formulae and their derivations, as well as in their physical interpretation, by the use of this algebra. For this purpose some properties derived from three-dimensional algebra are needed, which could be equally well applied to other physical phenomena. Two-dimensional vector algebra is therefore of notable pedagogical interest.