Yes when turning right you should always check your blind spot.
If you fail to check your blind spot when turning right then there might be pedestrians or bicyclists that could step out in your blind spot which you could accidentally run over.
Always check your blind spot when turning right or even when turning left.
When driving a vehicle the blind spot is the area that is around the vehicle that cannot be directly observed by the driver of the vehicle.
It's called a blind spot because you cannot easily see or cannot see at all what is around you in that blind spot.
Blind Spots exist around vehicles other than cars and exist in a wide range of vehicles such as cars, trucks, motorboats, sailboats, and aircraft.
Adding a blind spot mirror to your drivers side and passenger side mirrors can help you improve the sight in those blind spots.
The blind spot mirrors are pretty cheap and well worth it and you can just peel and stick on the blind spot mirrors.