ABSTRACT
This chapter introduces two important operations on vectors, the scalar product and the vector product, and shows how they can be used to describe lines and planes in space. Of these operations the scalar product can be defined more generally in n-dimensional space and we also show how to do this since it often arises in applications. In using coordinate systems to solve problems one naturally adopts a system best suited to the particular problem, but there is one type of system which is of general importance: a rectangular coordinate system. A coordinate system is said to be rectangular if its basis vectors are mutually orthogonal vectors of unit length; they are said to form an orthonormal basis. By contrast, a general coordinate system is often described as oblique. A vector of unit length is called a unit vector.
