# What determines the direction of cross product resultant vector?

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?

• It is defined that way Apr 30 '16 at 16:49

• @kyczawon We could've defined cross product with $a\times b$ pointing the other way. The mathematical community has agreed, however, to use the convention which uses right-hand rule. Apr 30 '16 at 17:00