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Can exactly two planes intersect and the third plane does not intersect the other two?
Wiki User
∙ 12y ago
We don't think so. We reasoned it out like this:
-- Two planes either intersect or else they're parallel.
-- If two planes intersect, then they're not parallel.
-- In order for the third one to avoid intersecting either of the first two,
it would have to be parallel to both of them. But if they're not parallel
to each other, then that's not possible.
If the third plane is parallel to one of the first two, then it's not parallel
to the other one, and it must intersect the one that it's not parallel to.
Wiki User
∙ 12y ago
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What do you call two planes that intersect?
Two planes that intersect are simply called a plane to plane intersection. When they intersect, the intersection point is simply called a line.
What plane has the two number lines that intersect?
Think about it, the x & y planes intersect and what one number has both, the x & y planes intersect. 0 on the coordinate plane is the, origin.
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.
If two planes intersect than they intersect at exactaly one point?
Yes. If two planes are not coincident (the same plane) and are not parallel, then they intersect in one straight line.
Can two planes intersect a third plane without intersecting each other?
Yes. Provided the first two planes are parallel, the third plane can be arranged so that it intersects both of the others.
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.
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.
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...
What is parallel planes?
Lines in the same plane that do not intersect Lines in the same plane that do not intersect Lines in the same plane that do not intersect Lines in the same plane that do not intersect
What do you call two planes that intersect?
Two planes that intersect are simply called a plane to plane intersection. When they intersect, the intersection point is simply called a line.
Can Two planes can intersect in exactly one point?
The intersection of two planes is a line. (or a massive explosion...lol)
What plane has the two number lines that intersect?
Think about it, the x & y planes intersect and what one number has both, the x & y planes intersect. 0 on the coordinate plane is the, origin.
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.
When two planes intersect do they intersect in a straight line?
Yes. If two planes are not coincident (the same plane) and are not parallel, then they intersect in one straight 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 rays need to be on the same plane to intersect?
Not necessarily. If two rays are on different planes, but the planes intersect, it is possible that the rays would also intersect, but the plane intersection would have to happen where the rays are located.
Can intersecting planes always intersect in exactly one point?
The intersection of two planes is never a point. It's usually a line. But if the planes have identical characteristics, then their intersection is a plane. And if the planes are parallel, then there's no intersection.
