Proving Velocity Vector Magnitude Equals c

[Pual Black]

Homework Statement

show that $V\prime=\sqrt{ V_{x}^\prime{ ^2} + V_{y}^\prime{ ^2} + V_{z}^\prime{ ^2}} = c$ -------------1

Homework 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

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
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[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.

 

[Pual Black]

Ok thank you for your answer. I must collect some more information and will post my results if i get some