Textbook Problem

Multiple operators can act on a function. If ${\stackrel{⌢}{P}}_x$ acts on the coordinate $x$ to yield $-x$, ${\stackrel{⌢}{P}}_x$ acts on the coordinate $y$ to yield $-y$, and ${\stackrel{⌢}{P}}_x$ acts on the coordinate $z$ to yield $-z$, evaluate the following expressions written in terms of $3\text{-D}$ Cartesian coordinates:

(a) ${\stackrel{⌢}{P}}_x\left(4,5,6\right)$

(b) ${\stackrel{⌢}{P}}_y{\stackrel{⌢}{P}}_z\left(0,-4,-1\right)$

(c) ${\stackrel{⌢}{P}}_x{\stackrel{⌢}{P}}_x\left(5,0,0\right)$

(d) ${\stackrel{⌢}{P}}_y{\stackrel{⌢}{P}}_x\left(\pi ,\pi /2,0\right)$

(e) Does ${\stackrel{⌢}{P}}_x{\stackrel{⌢}{P}}_y$ equal ${\stackrel{⌢}{P}}_y{\stackrel{⌢}{P}}_x$ for any set coordinates? Why or why not?