# Physics 511A, 2013: Chapter 1, Volume 2. The principle of relativity

2. Prove that ${\displaystyle \int _{a}^{b}ds}$ is maximal if taken along a straight world line that connects ${\displaystyle a}$ and ${\displaystyle b}$.
4. Suppose we denote a matrix that performs the Lorentz transformation as ${\displaystyle L({\vec {v}})}$. Do Lorentz transformations commute? That is, is ${\displaystyle L({\vec {v_{1}}})L({\vec {v_{2}}})}$ equal to ${\displaystyle L({\vec {v_{1}}}+{\vec {v_{2}}})}$?
6. Prove by direct computation that ${\displaystyle u_{i}w^{i}=0}$.