[QUE/QFT-06006 QFT-PROBLEM

Let \(p^\mu\) be a time like momentum vector. Let \(n^\mu\) be a four vector such that \begin{equation} n^\mu p_\mu=0, \text{ and } n^\mu n_\mu=-1. \end{equation} How many such independent four vectors \(n^\mu\) exist? How that the operators \begin{equation} \Pi^\pm_n =\frac{1}{2}\big(1\pm \gamma_5 n\!\!\!{n}\big) \end{equation} are projection operators satisfying. \begin{equation} \Pi^{(+)2}_n = \Pi^{(-)2}_n = I, \qquad \Pi^{(+)}_n \Pi^{(-)}_n =0. \end{equation} The notation here is same as in Bjorken and Drell, Gasiorowicz.