Vectors

Abstract

There are many examples in physics of quantities for which it is necessary to specify both a length and a direction. These include force, velocity and displacement, for example. Such quantities are modelled in mathematical terms by the concept of a vector. As so often happens in mathematics, the abstracted mathematical idea is more widely applicable than might have been imagined from the specific examples which led to its creation. We will see later that a further abstraction of our ideas produces a concept of even greater utility and breadth of application, namely that of a vector space. For the time being, in this chapter we will restrict our applications to the study of lines and planes in solid geometry, but the vectors used will be no different from those employed in mechanics, in physics and elsewhere.