Why does angular momentum point up for a counterclockwise rotation? Why not down? I am a high school student, and lately, I am founding things a bit perplexing on some topics concerning cross product in physics. In angular momentum, we learned that the direction of an object rotating clockwise would go down (we can use a helicopter as an example). Then, in a magnetic field, we were introduced to a moving charge in a magnetic field and experiencing a force in the direction perpendicular to the plane formed by the velocity and the magnetic field. In both situations, we implemented the right-hand rule to determine the direction. My question is why not the other way, down if up, and the converse? why does a proton go up when a magnetic field is to the right/east and a charge is moving perpendicular to a magnetic field north/up(in-plane sense)? Why does nature prefer these things? Is there something of symmetry? am I wrong to put such kind of question forward? Is there up and right for nature that it understand? 
I know that it is a convention and that it holds true. But how does nature identify right and left, and assign a product with a specific direction? 
 A: This is, in some sense, a matter of definition more than it is a matter of the fundamental nature of things.
For instance, in the case of angular momentum, I could easily define it to be $\textbf{L}=\textbf{p}\times\textbf{x}$, which would simply be the negative of the traditional definition. This is a perfectly fine definition of angular momentum: it is still conserved when the system is rotationally invariant, and could be related to a new definition of torque $\boldsymbol{\tau}=\dot{\textbf{L}}$, and everything would still be perfectly well defined. Positive angles would have to be defined as clockwise, not counterclockwise, and every equation you see when you open your physics textbook would still hold. The minus sign is completely arbitrary, as long as define your quantities in a way that is consistent.
In the case of the magnetic field, the Lorentz force $\textbf{F}=q\,\textbf{v}\times\textbf{B}$ could easily have been defined as $\textbf{F}=q\,\textbf{B}\times\textbf{v}$ if we simply redefined the magnetic field to be negative what we currently think of it as, or if we instead defined an electron to have a negative charge. It's all convention.
Nature doesn't care how you describe it. As long as you're consistent, then changing conventions shouldn't change any prediction.
As for the helicopters, you should note that French helicopters turn the other way.
I hope this helps!
A: There is no explanation why nature behaves as it behaves. We just observe it is right hand and no left hand.
