In Euclidean space, they could intersect along their whole lengths (in the lines are identical), at a point if they are coplanar and not parallel, or nowhere if they are parallel or skew.
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Two lines intersect at a point
Two lines that do not intersect on the same plane are Parallel lines.
are two lines that are not parallel, coplanar, and do not intersect
If two different lines intersect, they will always intersect at one point.
Two lines cross or intersect at a point.