The following section uses the Cartesian coordinate system with basis vectors e 1 = ( 1 , 0 , 0 ) , e 2 = ( 0 , 1 , 0 ) , e 3 = ( 0 , 0 , 1 ) and assumes that all vectors have the origin as a common base point. A vector a will be written as a = a 1 e 1 + a 2 e 2 + a 3 e 3 .