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Q.

A ray of light comes along the line Z = 0 and strikes the plane mirror kept along the plane P = 0 at B. A(2,1,6) is a point on the line Z=0 whose image about P=0 is, A'. It is given that L=0 is  x−23=y−14=z−65  and p= 0 is x+y-2z=3.The coordinates of A' areThe coordinates of B arelf  L1=0 is the reflected ray, then its equation is

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a

(6,5,2)

b

(6,5,-2)

c

(6,-5,2)

d

none of these

e

(5,10,6)

f

(10,15, 11)

g

(-10,-15,-14)

h

none of these

i

x+104=y−54=z+23

j

x+103=y+155=z+145

k

x+104=y+155=z+143

l

none of these

answer is , , .

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Detailed Solution

Let Q(x2,y2,z2) be the image of A(2, 1, 6) about mirror x + y -22 - 3. Then, x2−21=y2−11=z2−6−2=−2(2+1−12−3)12+12+22=4⇒x2,y2,z2≡(6,5,−2)let  x−23=y−14=z−65=λx=2+3λ,y=1+4λ,z=6+5λ lies on plane x+y−2z=3⇒2+3λ+1+4λ−2(6+5λ)=3or  3+7λ−12−10λ=3 or −3λ=12 or λ=−4 Point B≡(−10,−15,−14) The equation of the reflected ray L1 =0 is the line joining Q(x2,y2, z2) and B(- 10, - 15, - 14). x+1016=y+1520=z+1412or  x+104=y+155=z+143
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