The corner of a room is the intersection of two adjacent walls.
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Not really. A railroad intersection would be an example of two lines intersecting. An example of two planes intersecting would be the ground and the side of a building or the ground and the railroad crossing sign post.
In building construction, you usually have one horizontal plane (that floors) that is intersected by a vertical plane (the walls or support beams).
The Equator is a real world example, being the circumference of the Earth.
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