Can a plane be perpendicular in two other planes if those planes are not parallel to each other?

Question

I have to write equation of a plane which passes through a point and its perpendicular to 2 planes , but before I start solving I was thinking if can a plane be perpendicular to two other planes , if those 2 others are not parallel to each other ( linearly dependent) ?

Think of the planes XY, XZ, and YZ. They are all pairwise perpendicular, and no two of them are parallel. — Ivan Neretin, Jan 26 '18 at 14:21
Sorry, I don't follow. What would be possible? There are no planes in 2D, to begin with. — Ivan Neretin, Jan 26 '18 at 14:32
I meant to say wouldn't* be possible, isn't a sheet a 2d plane ? — Johnny Adams, Jan 26 '18 at 14:38
OK, there is *only one* plane in 2D. Surely it wouldn't be perpendicular to any other plane, because there is no other plane. — Ivan Neretin, Jan 26 '18 at 14:44
I mean a 2d plane not a 2d plane in a 2d world , because yes there would be just one 2d plane in a 2d world but there can be infinity 2d planes in a 3d world — Johnny Adams, Jan 26 '18 at 15:53
If you mean 2D planes in a 3D world, then we are back at my first comment. Yes it is possible that a plane is perpendicular to two other planes. — Ivan Neretin, Jan 26 '18 at 15:58

score 2 · Accepted Answer · answered Jan 26 '18 at 17:03

2

Yes: take two perpendicular planes, and a third plane perpendicular to their intersection.

For instance: with an orthonormal basis in $\mathbf R^3$, the $(x\text{-}y)$, $(y\text{-}z)$ and $(x\text{-}z)$ planes.

answered Jan 26 '18 at 17:03

Bernard

175,478

Indeed, take any two non-parallel planes, and take a plane perpendicular to their intersection. – John Gowers Jan 26 '18 at 17:08
That's true, but I wanted to point the planes can be pairwise perpendicular. – Bernard Jan 26 '18 at 17:10

Can a plane be perpendicular in two other planes if those planes are not parallel to each other?

1 Answers1