# Lorentz Velocity Transformation

## Homework Statement

Consider a light signal propagating in some arbitrary direction, with

vx $\neq$ 0
vy $\neq$ 0
vz $\neq$ 0 and

vx2 + vy2 + vz2 = c2

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

v'x2 + v'y2 + v'z2 = c2

## Homework Equations

Combination of Velocities

v'x = (vx - V)/(1-vxV/c2)

v'y = (vy√1-V2/c2))/(1-vxV/c2)

v'z = (vz√1-V2/c2))/(1-vxV/c2)

## 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.