The authors apply the image space approach to the analysis of the vector quasi-equilibrium problem (VQEP), especially to the saddle point conditions and gap functions associated with this problem. First they analyse the general features of the image space approach for the VQEP and to the linear separation arguments. The linear separation in the image space is characterized in terms of a saddle point and Kuhn-Tucker type conditions for a suitable Lagrangian function associated with the VQEP. In the last part, it is shown how the separation techniques in the image space can be used to define a gap function for the VQEP.