Correct!

Contrast this with another possible choice. what would happen if n were scaled by a linear function of n, e.g. a/2 x n ?

A third possibility is that used by rotation vectors: to scale by tan(a/2). While useful for eye movements (which do not normally rotate more than 50 deg.) the fact that this function explodes at 180 deg. makes it unsuitable for things that make large rotations (such as combined eye head and body rotations)