Linear Algebra/Hyperplanes

A hyperplane H is any subspace of R^n$$$$ of dimension n-1. The orthogonal complement of H is a subspace of dimension 1 (i.e. a line through the origin). Assume H orthogonal is spanned by a vector v_1 then an equation of H is given by OP.v_1 = 0 where P is any point in H.