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I have to prove if two lines intersect then they intersect in no more than one point I have to assume that lines intersect in MORE than one point i have to prove tht they intersect MORE than 1 wrong?
wrong!
Can 3 planes intersect at only 1 point?
No, they can intersect at infinitely many points.
Counterexample for two lines in a plane always intersect in exactly one point?
Line #1 ==> Y = x Line #2 ==> Y = x + 1 These two lines are parallel, have no points in common, and never intersect. (3 ways to say the same thing)
How many sides the cross have?
A cross has 1 side. And that side is the point that the 2 lines share.
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.
