please solve the question

Given an orthonormal basis {|1), |2) } in the state space, we define a new basis {lu), lv) } where lu) = all) + b|2). (1) Find the condition on a,b ensuring (u) a norm of 1. (2) Define the state [v) so that the new basis will be orthonormal. (3) Represent the projection operators on the states lu), (v) in the {|1), 12) } basis. (4) Could there be other answers to parts (2) and (3)? (5) Write down the transition matrix from the standard basis to the new basis. (6) Express the state () = 3|1) + 7|2) in the new basis