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the mirror image of point (3,1,7) with r...

the mirror image of point `(3,1,7)` with respect to the plane `x-y+z=3` is `P`. then equation plane which is passes through the point `P` and contains the line `x/1=y/2=z/1`.

A

`x+y-3z=0`

B

`3x+z=0`

C

`x-4y+7z=0`

D

`2x-y=0`

Text Solution

Verified by Experts

The correct Answer is:
C
Let image of `Q(3,1,7)w.r.t. x-y+z=3` be `P(alpha,beta,gamma).`
`:." "(alpha-3)/(1)=(beta-1)/(1)=(gamma-7)/(1)=(-2(3-1+7-3))/(1^(2)+(-1)^(2)+(1)^(2))`
`implies" "alpha-3=1-beta=gamma-7=-4`
`:." "alpha=-1,beta=5,gamma=3`

Hence, the image of Q(3, 1, 7) is P(-1, 5, 3) and

`implies" "|{:(x-0,y-0,z-0),(1-0,2-0,1-0),(-1-0,5-0,3-0):}|=0`
`impliesx(6-5)-y(3+1)+z(5+2)=0`
`:." "x-4y+7z-0`
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