N-dimensional vectors

We denote by \(V_2\) the set of all two-dimensional vectors and by \(V_3\) the set of all three-dimensional vectors. More generally, we will later need to consider the set \(V_n\) of all n-dimensional vectors. An n-dimensional vector is an ordered n-tuple: \[ \mathbf{a} = \langle a_1, a_2, ..., a_n \rangle \] where \(a_1, a_2, ..., a_n\) are real numbers that are called the components of a. Addition and scalar multiplication are defined in terms of components just as for the cases \(n = 2\) and \(n = 3\).