'3D Vector defined by 2 angles around a normal

I'm having trouble with a part of a school project of mine.

I need to find the vector v defined by the angles alpha and beta, but relative to a normal n instead of relative to the z axis.

I saw this question and answer, but it's only relative to the z axis, and I'm having trouble understanding how I can find v around a normal instead: 3D Vector defined by 2 angles

Thank you

vectorlinear-algebrapolar-coordinates


Solution 1:[1]

You need two vectors, if you give me the normal vector and an angle between the point and that vector, that can be satisfied by a family of points that lie in a circle.

Then you need a second vector to determine which point is the correct one.

Sources

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Source: Stack Overflow

Solution Source
Solution 1 Bob

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