Discriminantal Arrangement, $3\times 3$ Minors of Pl\"ucker Matrix and hypersurfaces in Grassmannian $Gr(3,n)$

We show that points in specific degree 2 hypersurfaces in the Grassmannian $Gr(3,n)$ correspond to generic arrangements of $n$ hyperplanes in ${\mathbb{C}}^3$ with associated discriminantal arrangement having intersections of multiplicity three in codimension two.