Why do you use the right hand for shaking hands?

Answer 1

For most people, it is there dominant hand, and that is just the way it has been done for centuries. Its probably the same reason why its the same hand we have over our hearts when we say a national anthem.

The dominant hand is/was also used to weild weapons which is the root of why we use that hand in a greeting of peace and welcome. In the days when it was not safe to be outside the walls of your city one was more likely to be holding a weapon with the dominant hand when meeting someone along the way. If that person was safe or peaceful you could put your weapon away. For those who you knew already you could raise your right hand without weapon in it as a greeting - the Romans used this as a salute in the military that is the origin of the current military salute. The raised empty hand and grasping hands is the civilian version of that peaceful greeting.

approximately 11% of the World's population is left handed