If w is a subspace of r n , show that w ∩ w⊥ = {0}. hint: start from definition, no complicated computation, it’s just some simple logic. note that if u · u = 0, then u must be a zero vector. also, both w and w⊥ are vector spaces, hence {0} ⊂ w ∩ w⊥ is clear, you just need to show another inclusion.