There is only one such plane.
1
four.
The intersection of three planes can be a plane (if they are coplanar), a line, or a point.
There is a subtle distinction between Euclidean, Hilbert and Non-Euclidean planes. Euclidean planes are those that satisfy the 5 axioms, while Non-Euclidean planes do not satisfy the fifth postulate. This means that in Non-Euclidean planes, given a line and a point not on that line, then there are two (or more) lines that contain that point and are parallel to the original line. There are geometries where there must be exactly one line through that point and parallel to the original line and then there are also geometries where no such line contains that point and is parallel to the original line.Basically, the fifth postulate can be satisfied by multiple geometries.
No, perpendicular planes intercept at only one point. Parallel planes do not intersect at all.
1
1
exactly 1
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Anything that contains the line must contain every point on the line, so "a point on the line" doesn't give us any more information. You're just asking how many planes can contain the line. Now imagine setting a wood panel down on a tight-rope. How many different ways can it set there before it falls off ? A lot, right ? An infinite number of planes can all contain your line. (And all of its points.)
four.
3
Only one plane can contain three specific points.
yes, three planes can intersect in one point.
Parallel planes.
No, planes intersect at a line.
The angle between two planes when the planes intersect at a point is the acute angle fixed by the normal vectors of the planes.