A minimum set of vectors that , through some combination of addition and multiplication , can reach any point in the vector space is called a basis of that vector space . The operations of vector addition and scalar multiplication have to satisfy certain requirements , called axioms , listed below . An example of a vector space is that of Euclidean vectors which are often used to represent physical quantities such as forces : any two forces ( of the same type ) can be added to yield a third , and the multiplication of a force vector by a real factor is another force vector .