Q: How many half planes does a line on a plane form?

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If I understand the grammar correctly, the answer is one line.

A single line is not sufficient to define a plane. You can find a plane such that the line is in it. But if you then rotate the plane using that line as the axis of rotation, you can get an infinite number of planes such that the line belongs to each and every one of the planes.

The intersection of two planes is a line. (or a massive explosion...lol)

Yes. If points are on the same side of a line, they are in a half-plane.

Yes. If two planes are not coincident (the same plane) and are not parallel, then they intersect in one straight line.

Related questions

-- A line has no plane and no part of one. -- Regarding a plane, go back and look at that word "half" again.

boundary line

If I understand the grammar correctly, the answer is one line.

Just 1 1 plane is simply a never ending line with absolutely no width or height. 2 planes would be a flat surface with no height

If you mean "only one plane can pass through another plane and through a point that is not on the line formed by the intersection of the two planes," the answer is "no." If you rotate the plane about the point, it will still intersect the line unless it is parallel to the line. By rotating the plane, you have created other planes that pass through the unmoved plane and through the point that is not on the line formed by the intersection of the two planes.

A single line is not sufficient to define a plane. You can find a plane such that the line is in it. But if you then rotate the plane using that line as the axis of rotation, you can get an infinite number of planes such that the line belongs to each and every one of the planes.

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.

A line. Unless the two planes are the same, in that case a plane.

The intersection of two planes is a line. (or a massive explosion...lol)

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.

Two planes that intersect are simply called a plane to plane intersection. When they intersect, the intersection point is simply called a line.

Yes. If points are on the same side of a line, they are in a half-plane.