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vector - 3D coordinates given two angles

Here's my problem.

vector angles

I have the angles alpha and beta on both xz and yz plane like the picture above. What I want to retrieve are the x,y and z coordinates of the vector. Is there any formula that is intended to do this? I found one that uses tangents but it's not suitable for my application because it may diverges to very high values. Thanks in advance.

question from:https://stackoverflow.com/questions/65916558/3d-coordinates-given-two-angles

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