Under the fitting headline "Example of Garbage Mathematics" Evans repeats his claim of the Lorentz transformation of the unit vector in boost direction
k = k'
on his blog site. Since Evans likes to refer to S.M. Carroll's Lecture Notes on General Relativity I recommend to Evans to have a look at the figure taken from p.7 where for a Lorentz boost in x/x'-direction the corresponding unit vectors i and i' are displayed: Evidently both vectors are different, so also k ≠ k' in case of a Lorentz boost in z/z'-direction.
