A mirror and a source of light are situated at the origin O and a point on OX respectively. A ray of light from the source strikes the mirror and is reflected. If the Dr's of the normal to the plane are 1,−1,1, then dc's of the reflected ray are
A
13,23,23
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B
−13,23,23
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C
−13,−23,−23
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D
−13,−23,23
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Solution
The correct option is C−13,−23,23 Let the source of light be situated at A(a,0,0), where a≠0.
Let OA be the incident ray and OB the reflected ray.
ON is the normal to the mirror at O.
∴∠AON=∠NOB=θ2(say)
d.r's of OA are a,0,0 and so its d.c's are 1,0,0
d.c's of ON are 1√3,−1√3,1√3
∴cosθ=1√3
Let l,m,n be the d.c's of the reflected ray OB.
Then l+12cosθ2=1√3,m+02cosθ2=−1√3 and n+02cosθ2=1√3