An inner product and an associated norm are defined on R² by the weighted scalar product where u = (2) and v = (u, v) 2u1v1 + 3u₂ v₂ = Let a = (²) and b = (a) Calculate (a, b), (a, a) and ||a|| (aa) b (b) Calculate the vector ca- (a,b) (c) Verify that, with respect to this inner product, the vector c is orthogonal to the vector a, but c is not orthogonal to the vector b