In recent years, there have been several reports on duality in vector optimization. However, there seems to be no unified approach to dualization. In the author's previous paper, a geometric consideration was given to duality in nonlinear vector optimization. In this paper, some relationship among duality, stability (normality) and condition of alternative will be reported on the basis of some geometric consideration. In addition, Isermann's duality in linear cases will be derived from the stated geometric approach.