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Yes, and in fact it is very likely that two planes will contain exactly one identical line. There are three possibilities:
- The planes are parallel, but not identical, in which case they contain no identical lines.
- The planes are not parallel, in which case they contain exactly one identical line.
- The planes are identical, and contain an infinite number of coplanar lines.
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Given a line and a point on that line how many different planes contain both of them?
1
What Point S is not on line k. How many different planes contain both point S and line k?
There is only one such plane.
Does intersection of 2 planes always contain at least 2 points?
YES. The intersection of two planes always makes a line. A line is at least two points.
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.
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.
How many planes contain a given line in space?
Given a line, there are an infinite number of different planes that it lies in.
Given a line and a point on that line how many different planes contain both of them?
1
Given a line and a point not on that line how many different planes contain both of them?
1
How many planes can contain a line and a point on the line?
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.)
What Point S is not on line k. How many different planes contain both point S and line k?
There is only one such plane.
How many planes can contain a line and a point not on the line?
exactly 1
How many planes can be drawn when three distinct points are collinear?
If the points are collinear, that means there's only one straight line. An infinite number of different planes can be drawn that contain one straight line.
Can Three distinct planes can intersect at a line?
Yes, it is possible for three distinct planes to intersect at a line.
How many planes can contain one specific line?
An infinite number of planes. Picture a line and now picture planes going in every direction through the line,
How many planes can contain two given points?
If 2 points determine a line, then a line contains infinitely many planes.
How many planes contain the same three collinear points?
Infinitely many planes may contain the same three collinear points if the planes all intersect at the same line.
How many planes can pass through line?
-- An infinite number of different planes can intersect the same line. -- The same line can lie in an infinite number of different planes. -- An infinite number of different lines can intersect the same plane.
