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Can a given line be in two planes?
Two planes intersect at a line. The line where they intersect pertains to both planes. In the same manner, if infinitely many planes intersect each other at the same line, then that line pertains to the infinitely many planes.
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.
What are the characteristics of parallel lines?
Parallel lines lying in a plane do not intersect each other. They share exactly zero points in common.
What is formed when two lines intersect?
Perpendicular lines are a possibility. This will only happen if the intersecting lines are exactly 90 degrees from each other.
Are all points of a cube coplanar?
Individual points on one side of the cube are coplanar. Points on one side might not nessasarily be coplanar with points on another side. The corners of a cube are exactly coplanar to three planes, but not all planes of the cube. In fact, no point on the cube is coplanar to all other points on the cube.
Where do two planes intersect?
In geometry, two planes intersect in a line. The only time this is not true is if the two planes are parallel to each other.
Can a given line be in two planes?
Two planes intersect at a line. The line where they intersect pertains to both planes. In the same manner, if infinitely many planes intersect each other at the same line, then that line pertains to the infinitely many planes.
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.
Can exactly two planes intersect and the third plane does not intersect the other two?
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.
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 two planes always intersect at only one point?
No, two planes do not always intersect at only one point. They can either be parallel and not intersect at all, or they can coincide, meaning they lie on top of each other and share all points. If two planes do intersect, they do so along a line, rather than at a single point.
Three planes that intersect in a point?
The intersection of three planes is either a point, a line, or there is no intersection if any two of the planes are parallel to each other. This tells us about possible solutions to 3 equations in 3 unknowns. There may be one solution, no solution, or infinite number of solutions.
Two lines that lie in paralell planes paralell?
Two lines that lie in parallel planes are not parallel to each other. While each line may be parallel to the plane it resides in, the fact that they are in different planes means they do not intersect and maintain a consistent distance apart, but they do not run in the same direction in three-dimensional space. Therefore, they can be considered skew lines, which are lines that do not intersect and are not parallel.
How do you sketch a three planes whose intersection is a point?
If you draw a capital "Y" with say each angle = 120 degrees, then the three lines will represent where the edges of the planes meet each other and the centre point will be the vertex where the three planes intersect. You are basically looking at the corner of a cube at an angle. If you connect the ends of the three lines you will be looking down at a triangular pyramid (three faces with three edges and the vertex in the centre).
What Straight line or planes that remain a constant distance from each other and never intersect are?
Parallel
If two lines intersect then they intersect in exactly one what?
If two lines intersect, they intersect in exactly one point. This point is the location where the two lines cross each other in a two-dimensional plane. In Euclidean geometry, two distinct lines can either intersect at one point or be parallel, in which case they do not intersect at all.
What does dihedral angle mean?
A dihedral angle is the angle between two intersecting planes.
