# Illustration Two Inertial Systems Move Relative to Each Other

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Two inertial systems $$S$$ and $$S'$$ with coordinates $$(c\,t, x,y,z)$$ and $$(c\,t', x',y',z')$$ move relative to each other with a constant velocity $$\boldsymbol{v}$$ in $$x$$ direction. A point $$P$$ has the position vector $$\boldsymbol{r}$$ in the $$S$$ system and the position vector $$\boldsymbol{r}'$$ in the $$S'$$ system.

The transformation of the coordinates from $$(c\,t, x,y,z)$$ to $$(c\,t', x',y',z')$$ is given by the Lorentz transformation (here: Lorentz boost).