A xy-plane is rotated about x and y-axis. But when it is rotated along z-axis, it doesn't change the orientation of xy-plane, why?
I've tried to find the answer but those answer that i found didn't have main reason.
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$\begingroup$Rotation around an "axis" is an illusion brought on by the fact that we live in three dimensions. Rotation is really around 2D planes.
In 2D, there is one plane: the space itself. So rotation is more of a back and forth.
In 3D, every 2D plane corresponds to a perpendicular direction and vice versa. This direction is the "axis".
When you rotate around the z-axis, you're really rotating around the xy-plane. The xy-plane itself is naturally invariant under this rotation.
In higher dimensions, you can rotate around more than one plane simultaneously.
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