How to draw a trajectory of a point in 3D space which moves on a surface of a sphere using Python?

Question

I have a line in 3D space. I will name it as OA. The point O is always (0,0,0) and A is (x1, y1, z1). Thus, the length(size) of the line is fixed. However, the angles it makes with X-axis, Y-axis and Z-axis can change.

1. What is the trajectory of point A? Is it a sphere?
2. If so how can I draw the movements of point A, when it is moving by changing the angles with each axis? (I have to do this by using Python)

I need to model the movement of the line and the movement of point A (which I think moves on a surface of a sphere) using Python.

I tried to break down the problem. If I am correct with the trajectory, what I have to do here is to generate values for x,y and z when xˆ2 + yˆ2 + zˆ2 = |OA|ˆ2.

Are there any known Python libraries that I could use for this?

Next, are there any Python libraries that I could use to build the model (GUI)?