U is a euclidean vector space, <.|.> the euclidean dot product on U, and f a linear functional on U.

1. prove that there exists a vector c_f in U such that f(x)=<x|c_f> for all x in U (hint: what is dim (N(f)) ?

2. is N(f) the orthogonal complement of any subspace of U? if so, which subspace?