Step 1: Assign B and G to Swift.
Since B and G are already specified to travel in the Swift, we place them there.
Step 2: Assign A and F to Creta.
Since A is not an engineer and travels in the Creta, F must be an engineer because the professions cannot repeat in the same vehicle.
Step 3: Assign the remaining passengers.
C, being a lady doctor, cannot travel with A and F, so she must travel in the Nexon. D, a male doctor, will also travel in the Nexon with C. Finally, E, being the remaining teacher, will also travel in the Nexon.
Thus, the profession of F is an Engineer.
Therefore, the correct answer is option (a).