Based on the parallelogram law, show that the norms ||.||_1 (1-norm) and ||.||_infinity ( infinity or maximum norm) in R^2 are not induced by any inner product.
Parallelogram Law: ||u+v||^2 + ||u-v||^2 = 2||u||^2 + 2||v||^2.
||x||_1: = sum i = 1 to n of |x_i|
||x||_infinity := max ( 1 =< i =< n)|x_i|