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Can three planes all intersect in the same line?
Yes they can. In fact, infinitely many planes can intersect in one line, at least theoretically.
Can two planes in three-dimensional space intersect at one point?
No, they intersect at a line.
If two different planes intersect then they intersect at one and only one line?
Yes, if two different planes intersect in three-dimensional space, they do so along one and only one line. This is because the intersection of the two planes consists of all points that satisfy the equations of both planes simultaneously, which geometrically forms a line. If the planes are parallel, they do not intersect at all, and if they are coincident, they overlap completely, but in the case of two distinct planes, the line is the unique intersection.
What would serve as a counter example to the statement Two planes intersect in exactly one line?
Two planes do not intersect at all if the planes are parallel in three-dimensional space.
When two planes intersect they intersect in one and only one?
When two planes intersect, they do so along a line, which is the locus of points common to both planes. This means they do not intersect at just one point but rather along an entire line. If the two planes are parallel, however, they will not intersect at all. Thus, the statement is incorrect; they intersect in a line, not a single point.
Can three planes all intersect in the same line?
Yes they can. In fact, infinitely many planes can intersect in one line, at least theoretically.
Can two planes in three-dimensional space intersect at one point?
No, they intersect at a line.
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...
Can two planes in three dimensional space intersect at one point?
No, the two planes intersect at a line, which is an infinite number of points.
Is it true that three planes can intersect in only one point?
The intersection of three planes can be a plane (if they are coplanar), a line, or a point.
Can three planes intersect in a point?
yes, three planes can intersect in one point.
What would serve as a counter example to the statement Two planes intersect in exactly one line?
Two planes do not intersect at all if the planes are parallel in three-dimensional space.
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.
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.
How many Two planes intersect in exactly?
Two distinct planes will intersect in one straight 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 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.
