Maths-

General

Easy

Question

# Let two planes and are given On the basis of the above information, answer the following question: The image of plane P_{1} in the plane mirror P_{2} is

- x+7y-4z+5=0
- 3x+4y-5z+9=0
- 7x-y+4z-9=0
- none of the above

Hint:

### Obtain the plane representation of the given lines and then obtain the mirror image of the plane.

## The correct answer is: 7x-y+4z-9=0

### Given That;

Let two planes and are given On the basis of the above information, answer the following question: The image of plane P1 in the plane mirror P2 is

>>> Let P3 be the plane which is the image of P1 in the plane mirror P2.

>>>The equation of P3 can be written as P1+λP2=0

⇒2x−y+z−2+λ(x+2y−z−3)=0

>> By inspection, (1,1,1) is a point on P1.

>>> Hence, the image of (1,1,1) across x+2y−z−3=0 must lie on the image plane P3.

Let the image of (1,1,1) in the plane P2 be (x′, y′, z′)

⇒x′−1/1=y′−1/1=z′−1/-1=−2(1+2−1−3)/1^{2}+2^{2}+1^{2}

⇒(x′, y′, z′)≡(4/3,5/3,2/3)

>>> Substituting this in the equation of P3, we get −1+λ3=0

⇒λ=1/3

>>> Hence, the equation of P3 is

2x−y+z−2+1/3 (x+2y−z−3)=0

⇒7x−y+2z−9=0

>>> Therefore, the equation becomes 7x-y+2z=9.

Therefore, the equation becomes 7x-y+2z=9.

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