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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.
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.
What are the characteristics of parallel lines?
Parallel lines lying in a plane do not intersect each other. They share exactly zero points in common.
What is formed when two lines intersect?
Perpendicular lines are a possibility. This will only happen if the intersecting lines are exactly 90 degrees from each other.
Are all points of a cube coplanar?
Individual points on one side of the cube are coplanar. Points on one side might not nessasarily be coplanar with points on another side. The corners of a cube are exactly coplanar to three planes, but not all planes of the cube. In fact, no point on the cube is coplanar to all other points on the cube.
