For simple Lie groups, matrix elements of vector operators (i.e. operators which transform according to the adjoint representation of the group) within an irreducible (finite-dimensional) representation, are studied. By use of the Wigner-Eckart theorem, they are shown to be linear combinations of the matrix elements of a finite number of operators. The number of linearly independent terms is calculated and shown to be at most equal to the rank l of the group. l vector operators are constructed explicitly, among which a basis can be chosen for this decomposition. Okubo's mass formula arises as a consequence.