Find the equation of the image of the plane $x-2y+2z-3=0$ in the plane $x+y+z-1=0$.

Question

I have no idea how to find the image of a plane in another plane.
Please help me.

what is your definition of imaging a point in some plane? :) I don't understand that what the question wants? :) Do you want to find the reflection of a plane with respect to another one? — Hosein Rahnama, Nov 19 '15 at 16:06

score 1 · Accepted Answer · answered Nov 19 '15 at 14:50

1

It is clear that the planes are not parallel, so they must intersect on a line. If we reflect one plane about the other, obviously it will too pass through this line.

Now the general equation of a plane passing through the intersection of the two planes is $x-2y+2z-3+t(x+y+z-1)=0$. The direction ratios of its normal are $(t+1,t-2,t+2)$.

Since we want the reflection, the new plane and the first should make equal angles with the second plane. Can you find $t$ from here?

answered Nov 19 '15 at 14:50

najayaz

5,459

Does imaging means reflecting? :) In fact, what the question is really asking? I am confused a little! :) – Hosein Rahnama Nov 19 '15 at 16:03
@H.R. a plane can be considered as a mirror, so yes, the 'image' of an object in it is really just the reflection. – najayaz Nov 19 '15 at 16:40
I just thought that imaging means projecting! :) – Hosein Rahnama Nov 19 '15 at 17:11

Find the equation of the image of the plane $x-2y+2z-3=0$ in the plane $x+y+z-1=0$.

1 Answers1