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A ray of light comes along the line L = ...

A ray of light comes along the line L = 0 and strikes the plane mirror kept along the plane P = 0 at B. `A(2, 1, 6)` is a point on the line L = 0 whose image about P = 0 is `A'`. It is given that L = 0 is `(x-2)/(3)= (y-1)/(4)= (z-6)/(5) and P =0 ` is `x+y-2z=3`.
The coordinates of B are

A

`(5, 10, 6)`

B

`(10, 15, 11)`

C

`(-10, -15, -14)`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
c
Let `(x-2)/(3)=(y-1)/(4)= (z-6)/(5)=lamda`
`" "x=2+ 3lamda, y=1 + 4 lamda, z=6+ 5lamda` lies on plane
`" "x+y-2z=3`
`rArr" "2+3lamda +1 +4lamda- 2 (6+5lamda)=3`
or `" " 3+7lamda-12-10lamda=3 or -3lamda=12 or lamda= -4`
Point `B-= (-10, -15, -14)`
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