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A plane mirror is placed at the origin so that the direction ratios of its normal are (1, -1, 1). A ray of light, coming along the positive direction of the x-axis strikes the mirror. Then the direction ratios of the reflected ray are

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a
13,23,23
b
−13,23,23
c
−13,−23,−23
d
−13,−23,23

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detailed solution

Correct option is D

Let (l, m, n) be the d.c’s of reflected ray We have (1, 0, 0) are the d.c’s of incident ray (x-axis).D.c’s of normal are 13,−13,13Let (l1,m1,n1)=(l,m,n),(l2,m2,n2)=(1,0,0)If θ is the angle between the normal to the plane and incident ray, then cosθ=13  l1+l22cosθ,m1+m22cosθ,n1+n22cosθ=(l,m,n)l+12cosθ=13⇒l=−13m−02cosθ=−13⇒m=−23  n+02cosθ=13⇒n=23

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