If we want to rotate a 2D vector we need only angle $\theta$ by which we want to rotate the vector. And we have only two possibilities: one for clockwise rotation and other for counterclockwise rotation. Pretty simple!
But things get complicated when we want to rotate 3D vectors. Mere giving an angle is not sufficient as we would have infinite possibilities for rotated vector. In fact, it is not hard to see that all possibilities of rotated vectors would make a cone, right?
So in 3D rotations we rotate a vector around a line, right?
But my problem is that I am not able to visualise how we are rotating a vector around a line. I don't need any rotation matrix or any other algebraic stuff. I just want to visualise the rotation through 3D diagrams.
It would be a great help if you spare some time to answer this question in detail.
You might simply take a 3D vector as an example, and show how we are getting a rotated vector around a line, for example z-axis.