A triangle? Three lines that intersect in three points.
In space with 3 or more dimensions, there are infinitely many pairs of lines that are not parallel and do not intersect.
There is an infinite number of lines.
Concurrent lines
Maximum 12 intersections are there! You can simply use the formula: No. of intersections = n(n-1)/2 [where 'n' is the number of lines] This is derived as each new line can intersect (at most) all the previously drawn lines. There if there is: 1 line => 0 intersections 2 lines => 1 intersection 3 lines => 3 intersections [1 that was there + 2 by the new line can intersect both the previous lines.] 4 lines => 6 intersections [3 that were already there + 3 because the new line can intersect all the 3 lines that were present previously.]
4
A triangle? Three lines that intersect in three points.
In space with 3 or more dimensions, there are infinitely many pairs of lines that are not parallel and do not intersect.
There is an infinite number of lines.
Concurrent lines
A triangle.
Send in the dots. We're ready.
They are asymptote lines in which as a curve gets closer and closer to them they will never intersect with each other.
Assuming that the none of the lines are parallel, they can intersect (pairwise) at three points. Otherwise, the question is tautological.
Maximum 12 intersections are there! You can simply use the formula: No. of intersections = n(n-1)/2 [where 'n' is the number of lines] This is derived as each new line can intersect (at most) all the previously drawn lines. There if there is: 1 line => 0 intersections 2 lines => 1 intersection 3 lines => 3 intersections [1 that was there + 2 by the new line can intersect both the previous lines.] 4 lines => 6 intersections [3 that were already there + 3 because the new line can intersect all the 3 lines that were present previously.]
intersection
- If you're working on a single sheet of paper (2-D), then you can draw four lines that intersect in 1, 2, 3, 4, 5, or 6 points. - If in 3-D space, then you can also draw four lines that don't intersect at all.