Is Angular Frequency a Vector or Scalar Quantity?

Angular frequency is the changes of angular displacement to the changes of time:

Therefore, if we say that the angular frequency is a vector, then an angle should be also a vector. In all reference books in physics, you can find that only a very small angles can be considered as a vector. But I am willing to tell you that there are several another factors (except very small angles) which can be defined as impact factors such as Amplitude of an oscillatory motion in which high amplitude does not allow you to use the rules dominated on vectors to analyze an oscillatory system with combination of many harmonic motions.

The surprising news is: "The most important impact factors are not very small angles and amplitude but the direction of the motion. In some situations and conditions, you can even consider a very large angle as a vector where this reverses the concept defined in reference books in Physics."

If you do not truly apply the concept of vector for angular frequency, the result of your analysis and design for an oscillatory system with combination of many harmonic motions, will go in wrong way.