1. The problem statement, all variables and given/known data The angular displacement θ, despite having a magnitude and a direction, cannot be treated as a vector. This is because θ does not follow the commutative law of vector addition. Does the infinitesimal displacement dθ obey the commutative law of addition and hence qualify as a vector? If so, how is the direction of dθ related to the direction of ω? 2. Relevant equations 3. The attempt at a solution That θ does not follow the commutative law of vector addition can be proved easily using an example of two rotations of some object. What I cannot prove is whether the the infinitesimal displacement dθ obeys the commutative law of addition. Any help on that would be greatly appreciated.