Suppose we have $D$ points in $D$ dimension, they lie on the same $D-2$-flat, and we associate each point a hyperplane that across through the origin.
For example, in three dimensional case, three data points $x_1,x_2,x_3$ lie on a line, and their corresponding vector is $v_1,v_2,v_3.$ Their corresponding hyperplane is $v_1\cdot x=0,v_2\cdot x=0, v_3\cdot x=0.$ ($v_i\cdot x$ means the inner product).
If $D$ points lie on a $D-2$-flat, how their corresponding hyperplanes related to each other.