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Er ...
So there are natural questions ...
... geometric questions about intersection of planes.
So how do you think two planes can possibly intersect?
Student: [...].
They may intersect along a line.
So you may have one plane and another plane.
And there is a common line ...
... as their intersection. That's a possibility.
Is that the only possibility?
What else is possible?
About two planes in 3-space.
Student: [...].
They can coincide. It could be just one plane.
That's a possibility. And what else?
So intersection is a line.
Or ...
... same planes ...
... produce a plane as intersection.
Is there anything else possible?
Student: [...].
A point of intersection.
So ...
Just one plane ...
... and another plane.
And they intersect at just one point.
So that's a possibility.
And what else?
Can they have no intersection?
Is that possible?
Is there anything ... any word you can use to describe this situation?
Student: They are parallel. NB: They are parallel.
So two planes can be parallel.
And then there is no intersection.
And is there anything else possible?
Student: Skewed. [...].
Skew.
Can [...] be skew?
So skew in terms of intersection what does that mean?
Does it mean no intersection?
No [...]. If no intersection it means they are parallel.
Can they be skew?
Skew giving no intersection but not being parallel.
[...] in doubts.
So ... Let's [...] a question. Skew planes.
Now how to answer those questions? How to ...
... verify that yes, indeed these are the only possibilities?