Another way to represent a vector in n -dimensions is to introduce the standard basis vectors. For instance, in three dimensions, there are three of them: e 1 = ( 1 , 0 , 0 ) , e 2 = ( 0 , 1 , 0 ) , e 3 = ( 0 , 0 , 1 ) . These have the intuitive interpretation as vectors of unit length pointing up the x -, y -, and z -axis of a Cartesian coordinate system, respectively. In terms of these, any vector a in R can be expressed in the form: a = ( a 1 , a 2 , a 3 ) = a 1 ( 1 , 0 , 0 ) + a 2 ( 0 , 1 , 0 ) + a 3 ( 0 , 0 , 1 ) ,