This is not a homework problem, but pertains to the class (Calculus II) that I am taking. I am very confused about how to think intuitively about determining orientation of a cross product. My understanding of the right hand rule in determining the orientation of the third axis is that by convention, if two axis are oriented positively in a certain way, then by convention the third should be pointed a specific way, and you use the right hand rule to determine this way. This makes sense to me. But when it comes to the cross product, I am so confused by the intuition behind determining the orientation of the vector. The textbook merely says that if you curl your fingers from a to b the direction that your thumb is pointed determines the direction of the cross product. Why? I have searched this question on the internet and on physics forums and still do not understand. I have seen responses that it is also a convention, but I guess I don't understand the motive for the convention. I do not have any physics background (well besides a intro mechanics class) that has used the right hand rule, so that may be part of the problem. The closest answer I saw to my question was here: http://www.scienceforums.net/topic/74133-what-is-the-intuition-behind-the-right-hand-rule/ ,but I am still confused. I guess my understanding right now is that when you cross two vectors, you get a vector perpendicular to that vector and because that vector could be oriented in either direction, we use the right hand rule to decide a direction so that we have a convention by which we can agree it is oriented? Why should ixk be oppisitelly oriented to jxi? Thank you in advance.