  We use the theory of vertex operator algebras and intertwining operators to
obtain systems of q-difference equations satisfied by the graded dimensions of
the principal subspaces of certain level k standard modules for
\hat{\goth{sl}(3)}. As a consequence we establish new formulas for the graded
dimensions of the principal subspaces corresponding to the highest-weights
i\Lambda_1+(k-i)\Lambda_2, where 1 \leq i \leq k and \Lambda_1 and \Lambda_2
are fundamental weights of \hat{\goth{sl}(3)}.
