(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Consider a light signal propagating in some arbitrary direction, with

v_{x}[itex]\neq[/itex] 0

v_{y}[itex]\neq[/itex] 0

v_{z}[itex]\neq[/itex] 0 and

v_{x}^{2}+ v_{y}^{2}+ v_{z}^{2}= c^{2}

Use the Lorentz transformation equations for the components of velocity to show that

v'_{x}^{2}+ v'_{y}^{2}+ v'_{z}^{2}= c^{2}

2. Relevant equations

Combination of Velocities

v'_{x}= (v_{x}- V)/(1-v_{x}V/c^{2})

v'_{y}= (v_{y}√1-V^{2}/c^{2}))/(1-v_{x}V/c^{2})

v'_{z}= (v_{z}√1-V^{2}/c^{2}))/(1-v_{x}V/c^{2})

3. The attempt at a solution

I know this is just a simple algebra proof but for some reason I'm getting stuck on it. Maybe I'm using the wrong equations?

I would really appreciate being shown where to start for this proof. Thanks in advance for the help and/or time.

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# Lorentz Velocity Transformation

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