Shift a position (latitude, longitude) by adding a vector

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Let us assume we have some position given in latitude and longitude decimal degrees. Now, we want to move this position by adding some vector given with some magnitude (length) and phase (direction).

Is it now correct to just convert the polar coordinates of the vector into Cartesian (x,y) coordinates and then to add the x,y to the latitude/longitude? Or is it not that simple since the geographic position is mapped to a 3D sphere (earth) and not a 2D plane?

And if it is not that simple, how would one do it correctly?