Suppose I have a sphere S spinning with some random rotation.
Suppose now I create a vector V from the center of S to any point of the space.
How can I get the magnitude of the rotation of S around V ?
You need to know what ‘zero’ is (1 vector) and then you can compare this with the ‘current’ (also 1 vector) by calculating the angle between those vectors after projecting them into the plane of which v is the normal vector. 
… sorry, cannot explain this less complicated