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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 (x,y,z) of
`therefore (x-3)/(1)=(y-1)/(-1)=(z-7)/(1)=-2((3-1+7-3)/(1^(2)+1^(2)+1^(2)))=-4`
`P(x,y,z)=(-1,5,3)`
plane passing through p(-1,5,3)is
`a(x+1)+b(y-5)+c(z-3)=0`
also plane contains line `(x)/(1)=(y)/(2)=(z)/(1)`
`therefore (0,0,0)`satisfy
`implies a-5b-3c=0`
`and a+2b+c=0`
from (2) and (3)
pin in `(1)(X+1)-4(y-5)+7(z-3)=0`
`or x-4y+7z=0`
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Knowledge Check

  • Let P be the image of the point (3, 1, 7) with respect to the plane x -y + z = 3 . Then, the equation of the plane passing through P and containing the straight line (x)/(1) = (y)/(2) = (z)/(1) is

    A
    `x + y - 3z = 0`
    B
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    C
    `x - 4y + 7z = 0`
    D
    `2x -y = 0`

  • The plane, which passes through the point (3,2,0) and line (x-3)/(1)=(y-6)/(5)=(z-4)/(4) is

    A
    `x-y+z=1`
    B
    `x+y+z=5`
    C
    `x+2y-z=1`
    D
    `2x-y+z=5`

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