Problem 3 Let V be a Euclidean space. Prove that the next equalities hold for any two elements u, ve V 1 . |/ 4 0712 = 1/2112 + 110112 + (2, 0) + (8, 2) 2. |4 0512 - 170(-3)112 = 2(2, 0)+2(0, 2) 3. In particular, if we choose V = R2 with the usual internal and external operations, and with the inner product defined as (u, v) = 2u1v1 + u102 + u2v1 + 4u202 (1) where u = (u1, u2), U = (v1, v2), prove that the previous properties hold. 4. Given a vector w = (1, 0) find any orthogonal vector to w and plot both vectors in a Cartesian coordinate system