Demostrate that a light beam reflected from three mutually perpendicular plane mirrors in succession reverses its direction.

Explanation

we can assume three mutually perpendicular plane mirror
(x-y) plane Normal unit vector is `hatk`
(y - z) plane Normal unit vector is `hati`
(z - x) plane Normal unit vector is `hatj`
`hate_(1)`= a`hati` + b`hatj` + c`hatk` is a unit vector incident on The first mirror after reflection through
( x - y) plane mirror the unit vector of reflected ray. `hate_(2)` =a`hati` + b`hatj`- c`hatk` and this ray incidents on the mirror (y-z) plane and reflected ray
`hate_(3)` = `ahati` + `bhatj`- `chatk` and finally thisray incidents on the mirror (z - x) plane after reflection
`hate_(4)` =-`ahati`-`bhatj`-`chatk`
i.e. ` hate_(4)` = `-hate_(1)` this means, final ray reverses its direction