Prove that for all scalars: a, b k = that: sigma^n_k = 1 a_k b_k lessthanorequalto [sigma^n_k = 1 a^2_k]^1/2 [sigma^n_k = 1 b^2_k]^1/2 a. prove the parallelogram law: ||u + v||^2 + ||u - v||^2 = 2||u||^2 + 2||v||^2 b. explain why it is called the parallelogram law. prove: = 1/4 ||u + v||^2 - 1/4 ||u - v||^2 write the formula for the euclidean norm in e. show that 1/||v|| v is a unit vector. use the properties of a norm to show that the metric: d(u, v) = ||u - v||