In this paper we study intersections of quadrics, components of the hypersurface in Grassmannian $Gr(3, \CC^n)$ introduced in \cite{SoSuSi}. This lead to an alternative statement and proof of Pappus's Theorem retrieving Pappus's and Hesse configurations of lines as special points in complex projective Grassmannian. This new connection is obtained through a third purely combinatorial object, the intersection lattice of Discriminantal arrangement.