Let V be an inner product space and v, u,x,y,z EV such that vis orthogonal to u, x, y and z. Prove that v is also orthogonal to span{u.x,y,z}. (4) (b) Let u and v be orthogonal vectors. If u + vand u - v are orthogonal, show that | u ||=|| v ||. (5) (C) Given the vectors uz = (1,2,1,0), u2 =(3,3,3,0), u3=(2, -10,0,0), u =(-2,1,-6,2). i. Show that the vectors {ui, u2, 13, 14} form the basis for R4. ii. Use the Gram-Schmidt process to determine an orthonormal basis for the subspace of R"spanned by the given set of vectors {uj, u2, 13, 14} .