This paper deals with the vectorial formulation of variationally consistent sets of differential equations that, with either transverse shear or transverse normal deformation effects taken into consideration, govern the static and/or dynamic behaviour of homogeneous or inhomogeneous elastic plates. The present formulation is based on a general form of the displacement representation and yields the kinematic relations, constitutive equations and equations of motion of a variationally consistent, shear and normal deformable, general plate theory, the number of degrees of freedom, as well as the performance, of which can be controlled a posteriori. It is shown to be equivalent with a variational approach and can further be considered as a generalization of several variationally consistent transverse shear and normal deformable plate theories, in the sense that, in particular cases, it quotes their governing equations derived elsewhere variationally. Moreover, just as happens with the application of a variational approach, an a priori knowledge of the elastic law governing the material behaviour of the plate considered is not required. Under the general assumption that there exists a strain energy density function, the present vectorial approach can be applied successfully.