I have sets of multiple vectors, say 10.
I have calculated the angles that each vector forms on the xy, yz and xz planes (NOT with the plane (image) %Figure I used the atan2d function on Matlab, and also manually cacluated to have a positive angle over 360-degree rotation (Allowing for each quadrant)
Then I also calculated the mean vector in 3D (Using averaging the normalised vectors and sum over and normalising the result. Also done with quaternion averaging. I get the same result for the mean vector.
Then I calculated the angle that the mean vector forms in each plane, just like I did for individual vectors.
My question is should the arithmetic mean of the angles of individual vectors be similar to the angle that the mean vector forms in the same plane? I can see this being similar in some cases but not all. I have tried correcting for quadrants and adding 2π to angles where necessary. Works with some sets, not with others? Any suggestions pls