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where does a plane intersect in geometry?
A plane intersects a line at a point, and i plane intersects another plane at a line.
If two planes intersect do they intersect in exactly one plane?
No, two planes do not intersect in exactly one plane unless the planes are exactly overlapping, making one plane. In Euclidean Geometry two planes intersect in exactly one line.
Can a line and a plane intersect at exactly two points?
No, that isn't possible.
A plane and a line sometimes never or always intersect in a single point?
A given plane and a given line don't necessarily have to intersect at all.If the line is parallel to the plane, then they never do.The line can also be in the plane, and then every point on the line is alsoa point in the plane.The most likely case, though, is that the line is not parallel to the plane andnot in it. In that case, their intersection is a single point.So I guess the best answer from the allowed choices is 'sometimes'.
Can two different planes intersect a line?
Yes, there are three ways that two different planes can intersect a line: 1) Both planes intersect each other, and their intersection forms the line in the system. This system's solution will be infinite and be the line. 2) Both planes intersect the line at two different points. This system is inconsistent, and there is no solution to this system. However, both planes will still be intersecting the same line, albeit at different locations on the line. 3) Both planes intersect each other, but their intersection does NOT form the line in the system. However, if the line in the system intersects the planes' intersection, then they will all intersect a single point. The solution will be finite and be a single point. There are also 3 ways two different planes WON'T both intersect a line. 1) The two planes and the line are all parallel to each other, and none of them intersect each other. 2) The line is parallel to one plane, but intersects the other plane. 3) The same as #2, but now the line is parallel to the other plane and intersects the one plane.
