Intersecting Planes: Visualizing & Explaining

[RoughRoad]

I read somewhere that a line is formed as a result of intersection of two planes.

Now, I can't imagine it geometrically. Can someone help me visualise this? Or atleast explain me what it means?

 

[symbolipoint]

What you read is true. Why can you not visualize two planes intersecting? Make a physical model, or look for a physical model in the real world which fits this. The words can only take you to a limited extent; after that, you must think, and make drawings and try to build simple models.

 

[RoughRoad]

Is it something like two squares intersecting, and both sharing a common side?

 

[arildno]

Paddle wheel?

 

[HallsofIvy]

Look at a corner of the room you are sitting in. The walls are planes and they intersect on the line forming the corner.

 

[Mark44]

Look at a corner of the room you are sitting in. The walls are planes and they intersect on the line forming the corner.

I hope the OP isn't sitting in an igloo!

 

[mathwonk]

the size of the intersection of two objects depends also on the ambient space containing them. the bigger that space the more room they have to separate and the smaller is their intersection. So two planes in three space intersect either in a line l, like the dies of a boc meeting along an edge, or they coincide, thus intersecting in a plane, or they are parallel, and do not intersect at all, i.e. their intersection is empty.

but in 4 space, 2 planes can also intersect in a point. thus in linear algebra, two linear equations in 4 variables define a plane, so 4 equations define two planes and they can have a unique simultaneous solution.

 

[dav2008]

[PLAIN]http://mathwise.net/pages/geometry/Glencoe_Geometry_Notes_and_Tests/chapter_1_geometry_notes_files/image008.gif

 

[Mark44]

So two planes in three space intersect either in a line l, like the dies of a boc meeting along an edge,...

dies of a boc - ?

Maybe you're saying "sides of a box"

 

[John Mario]

I read somewhere that a line is formed as a result of intersection of two planes.

Now, I can't imagine it geometrically. Can someone help me visualise this? Or atleast explain me what it means?

To visualize it, take two pieces on carboard. Make a slit in each piece than connect the two pieces via the slits.

Each piece of carboard is a plane. The two planes meet at the slits. The intersection of the two planes is a straight line.