3D Rotation

I have used the idea that the end of a vector is a point on a sphere and the other end is the origin of the XYZ Axis of roation. I want to move the X-Axis DegX and the Y-Axis DegY and the Z-Axis DegZ.

How do I do the rotation calculation.

PS: Converting from 3D to 2D, I already have working, for plotting the vector, but the new XYZ coordinates of the Vector????????

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