A ray of light is incident on a plane mirror along a vector `hat i+hat j- hat k.`
The normal on incidence point is along `hat i+ hat j `.Find a unit vector along the
reflected ray.

Options

A. `1/sqrt(3)(hat(i) + hat(j) + hat(k))`
B. `-1/sqrt(3)(hat(i) + hat(j) + hat(k))`
C. `1/sqrt(3)(-hat(i) - hat(j) + hat(k))`
D. `1/sqrt(3)(-hat(i) + hat(j) + hat(k))`

Answer

B

Explanation

`hat( e)_(2)=hat(e )_(1)-2(hat(e_(1)).hat(n))hat(n)`
`=(hat(i) + hat(j) + hat(k))/sqrt(3) -2[((hat(i) + hat(j) + hat(k)))/sqrt(3) . ((hat(i) + hat(j)))/sqrt(2)]((hat(i) + hat(j)))/sqrt(2)`
=`-((hat(i) +hat(j) + hat(k)))/sqrt(3)`