Small Rotation about q: How \epsilon \vec{n} \times \vec{q} Works

[ehrenfest]

Homework Statement

My book says that $$\epsilon \vec{n} \times \vec{q}$$ represents a small rotation about q.
n is an normal vectors
Obviously the cross product is orthogonal to both n and q, but I did not know it corresponded to an angle?
BY the way, how do you make a cross product in tex?

Homework Equations

The Attempt at a Solution

 

[mjsd]

cross product in tex? \times will be fine

the epsilon correspond to the small amplitude of your infinitestimal rotation I think

 

[ehrenfest]

But why does this represents an angle?

 

[Dick]

It doesn't represent an angle. It represents an infinitesimal displacement. A small displacement from a vector q rotated around an axis along n should be perpendicular to both. Hence nxq.