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Point A lies outside of plane P. How many planes can be drawn parallel to plane P that pass through point A?
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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.
Which directions does a Parallel go?
If you mean a 'parallel' of latitude on the earth, then it is a circle that proceeds east and west from any point on it. There can be any desired number of them, the only specification being that every point on the 'parallel' has the same geographic latitude. Since these are all curved lines, it's hard to say that they are parallel in the same sense as parallel straight lines on a flat surface. But the planes they lie in are all truly parallel planes.
How many planes can pass through a point in space?
Infinitely many.
How many planes could pass through a point?
Infinitely many.
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.
What do you called the planes that have no common point?
Parallel planes.
Is it true that only one plane can pass through one and a point that is not on the line?
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.
Why hilbert axiom of parallelism assert the existence of only at most one parallel line'?
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.
Do two planes intersect in infinitely many points?
No, perpendicular planes intercept at only one point. Parallel planes do not intersect at all.
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.
Which directions does a Parallel go?
If you mean a 'parallel' of latitude on the earth, then it is a circle that proceeds east and west from any point on it. There can be any desired number of them, the only specification being that every point on the 'parallel' has the same geographic latitude. Since these are all curved lines, it's hard to say that they are parallel in the same sense as parallel straight lines on a flat surface. But the planes they lie in are all truly parallel planes.
How do you negate the euclidean parallel postulate?
Assume there are no lines through a given point that is parallel to a given line or assume that there are many lines through a given point that are parallel to a given line. There exist a line l and a point P not on l such that either there is no line m parallel to l through P or there are two distinct lines m and n parallel to l through P.
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.
How many planes can pass through a point in space?
Infinitely many.
How many planes could pass through a point?
Infinitely many.
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.
Why can rays be perpendicular but not parallel?
Rays pass through one point. Parallel lines never meet.
