# Theory of relativity

1. Dec 5, 2014

### Pual Black

1. The problem statement, all variables and given/known data
show that $V\prime=\sqrt{ V_{x}^\prime{ ^2} + V_{y}^\prime{ ^2} + V_{z}^\prime{ ^2}} = c$ -------------1

2. Relevant equations
$V_{x}^\prime{ ^2}=\frac{V_x - V }{1-{\frac{V V_x}{c^2}}}$ -----------------2

$V_{y}^\prime{ ^2}=\frac{V_y \sqrt{1-{\frac{V^2}{c^2}}}}{1-{\frac{V V_x}{c^2}}}$ ------------3

$V_{z}^\prime{ ^2}=\frac{V_z \sqrt{1-{\frac{V^2}{c^2}}}}{1-{\frac{V V_x}{c^2}}}$ -----------4

3. The attempt at a solution

i tried to just substitute the 3 equations (2,3,4) in eq. 1 but i didnt get the right answer

2. Dec 5, 2014

### Simon Bridge

There's not enough information. Usually there is some sort of context since, in general, the magnitude of the 3-velocity is not c.
Work through in order - starting from the full problem statement.

3. Dec 6, 2014