Why is the right hand rule for cross product?

[iScience]

so, the magnitude of the cross product represents the area or volume enclosed by any 2 or 3 vectors respectively, but what does the direction represent? i get that the general direction is one that is perpendicular to all the vectors, but what does the actual direction represent? ie, why the right hand rule? ie, why this particular direction instead of the opposite? is it just by convention or is there a particular reason?

 

[lurflurf]

The right hand rule is just a convention. If one adopts the left hand rule everything would work the same only backwards. This is to fit with the usual naming of the axes x,y,z.

 

[electricspit]

To expand on what lurflurf said, it is just a convention. The coordinate system most widely used is a right-hand coordinate system. You can see for yourself by using the right-hand rule on the x and y axes.

This would lead to the z-axis point towards you if the y-axis is oriented vertically and the x-axis oriented horizontally (in the plane perpendicular to your vision).

The right-hand rule just makes all the cross products you perform in this space conform to this.