1. The problem statement, all variables and given/known data Let V be an inner product space, and let W be a finite dimensional subspace of V. If x is not an element of W, prove that there exists y in V such that y is in the orthogonal complement of W, but the inner product of x and y is not equal to 0. 2. Relevant equations 3. The attempt at a solution I'm pretty lost. There is a theorem which states: Let W be a finite dimensional subspace of an inner product space V, and let y be in V. Then there exist unique vectors u in W andf z in the orthogonal complement of W such that y=u+z. But I don't know how this would apply.