Why do we use the right hand rule to determine the direction of the vector resulting from using the cross product? A resultant vector that was directed in the opposite direction would also be perpendicular to both vectors…
EDIT: If we cross a x b, using the right hand rule we use point our index finger in direction of a, the middle finger in direction of b, and we use the thumb to get the direction of c. From a mathematical point of view, why can't c point in the opposite direction to the thumb?
Best Answer
We have to pick one way to do it - either the right hand rule or the left hand rule. It's not important which one we use, as long as everyone uses the same one - just like which side of the road we drive on. We'd get the same eventual results if we all used the left hand rule. Someone chose the right hand rule over the left hand rule, and it became convention, so that's what we use.