A vertex? In non-euclidean geometry: A two distinct parallel lines intersect in the "Infinity zone"
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Parallel lines do not intersect.
parallel ============================================= Parallel. _____________________ _____________________ Those two lines will NEVER intersect.
Parallel lines are lines that never intersect. So the answer is no.
No. The planes must either coincide (they are the same, and intersect everywhere), be parallel (never intersect), or intersect in exactly one line.
The lines have to intersect because lines go on forever and if then are not parallel then they will collide. Even if they are not parallel by one degree they will still intersect.