$${\begin{align*}\dot z'&=\frac{\dot z-u}{1-\frac{\dot z u}{c^2} } \\ \dot y' &=\frac{\sqrt{1 - \left( \frac{u}{c}\right)^2}\dot y}{1-\frac{\dot z u}{c^2} } \\ \dot x' &= \frac{\sqrt{1 - \left( \frac{u}{c}\right)^2}\dot x}{1-\frac{\dot z u}{c^2} } \end{align*}}$$