Take two orthogonal vectors u, v ε R". u v, and let X = (Xi, , X,) be a vector of n iid standard Gaussians. Xi ~ N(0, 1), yl E「r). Let llr-〈II, X〉 and vr-(v, X〉, Are ux and vr independent? Hin: First try to see if they are correlated; you may use the fact that jointly normal random variables are independent iff. they are uncorrelated.
