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Two planes can intersect on exactly one point?
No, 2 planes may only intersect at a line, a plane, or not at all. THREE planes may intersect at a point though...
Three planes may all intersect each other at exactly one point?
Three planes may all intersect each other at exactly one point. This commonly occurs when there is one straight plane and two other planes intersect it at acute or obtuse angles.
Do two planes intersect in infinitely many points?
No, perpendicular planes intercept at only one point. Parallel planes do not intersect at all.
Can three planes all intersect in the same line?
Yes they can. In fact, infinitely many planes can intersect in one line, at least theoretically.
What would serve as a counter example to the statement Two planes intersect in exactly one line?
Two planes do not intersect at all if the planes are parallel in three-dimensional space.
Does three lines intersect at the same point must all be in the same plane?
No. Any pair of the three will describe a plane, so the three possible pairs describe three planes.
How many planes contain the same three collinear points?
Infinitely many planes may contain the same three collinear points if the planes all intersect at the same line.
Can two horizontal planes intersect?
No, horizontal planes run parallel to each other, so they do not intersect, but two vertical planes can intersect. Imagine the pages of a books as several planes. When you stand the book up, they are all vertical, but they all intersect at the book spine.
What is the maximum number of times 2 planes can intersect?
In three-dimensional space, two planes can either:* not intersect at all, * intersect in a line, * or they can be the same plane; in this case, the intersection is an entire plane.
Do Two planes always intersect in a line?
Some planes are parallel and don't intersect at all. Those that do intersect (and that are not coincident, i.e. the same plane) intersect in a line.
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.
Do planes intersect in exactly two points?
No. Either they do not intersect at all, or they intersect in a straight line or are the same.
