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## Homework Statement

Here's the question:

http://i.imgur.com/zs130b3.png

## Homework Equations

Just the usual Lorentz transform matrix etc.

## The Attempt at a Solution

http://imgur.com/4Oipfu9

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)

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