How to compute the amplitude of a sampled wave in three dimensional space

I have a sine or cosine wave in a random direction in 3D space and in a random orientation. I want to calculate the amplitude and axis for such a wave. I am sampling the wave at a high rate, compared to the frequency of the wave. I am getting the 6 DOF values for each sample.

I am looking for pointers on how to compute the amplitude and axis of the wave.