How can I solve a 3D coordinate problem involving rotation and a given point?

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The discussion centers on solving a 3D coordinate problem involving the rotation of a point (x0, y0, z0) around a line in the X-Y plane defined by an angle theta (0 - 360 degrees) about the Y-axis. The key challenge is determining the new position of the point after it is rotated phi degrees about this line. Participants noted that without a specific line, the problem lacks sufficient information for a definitive solution, and there was a debate regarding the correct range for theta, with suggestions that it should be limited to 0 <= theta <= 90 degrees.

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I have been thinking about this problem for awhile, but have no idea to even begin solving it. Was wondering if anyone has a clue to help me started?
There's a point (x0,y0,z0) in 3D. There is a line on the X-Y plane. This line is say theta degrees (0 - 360) about the Y-axxis. If the point (x0, y0, z0) is rotated phi degrees about this line, what is the new position?
This is just a problem I thought up, so I don't even know if there is enough information to solve it.
Please help me, let me know what's a good step to solve it? Should I use Cartesian system, or use another one?
Thanks!
 
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There are 'infinity' of lines that form the same angle with the y-axis. So if the exact line's not given, I don't think this is solvable.
Anyway, are you sure this statement is correct?
pimanian said:
say theta degrees (0 - 360)
Shouldn't that be 0 <= theta <= 90?
Viet Dao,
 

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