A cooling system for a gas turbine engine includes a first plenum, a first cooling flow passageway, and a second cooling flow passageway. The first cooling flow passageway is in fluid communication with the first plenum and with a first airfoil cooling channel within an airfoil of the stator vane. The first airfoil cooling channel is for cooling a leading edge of the airfoil. The second cooling flow passageway is in fluid communication with the first plenum and with a platform cooling channel within an outer diameter platform of the stator vane. The first cooling flow passageway and the second cooling flow passageway are disposed within a mounting hook. The first cooling flow passageway and the second cooling flow passageway are not in fluid communication with each other.