Here's the question:
Just the usual Lorentz transform matrix etc.
The Attempt at a Solution
Now, the last line is clearly incorrect, since it tends towards infinite relative speed as v --> c. Of course the initial answer of sqrt(2)v for the first part is fine because that isn't relative speed (I am pretty sure I have this part right - let me know if not). I have a feeling I can't 'Pythagorise' the 3-velocity part of Vrel4 to get a magnitude, but this is a bit of a guess. Vrel4 still seems to obey the V.V = (+/-)c^2 inner product identity so that points towards it being the correct 4-vector, although I may be wrong about that.
Thanks for any help.
(check the imgur links, pictures didn't work)