0
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.
Still curious? Ask our experts.
Chat with our AI personalities
Rene
Beau
TaigaAdd your answer:
Earn +20 pts
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.
