Lorentz Transformation with an Arbitrary Direction of Motion

we assumed that the S’frame
moves along the x direction
relative to the S frame.
Now suppose that’s not the case, and that the S’frame
moves with an arbitrary (but constant) velocity v relative to S. Find the Lorentz Transformation formula between the two frames, i.e., for an event (r, t) in the S frame,
what is the corresponding expression for the same event (r’, t’) in the S’frame?
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