The intersection of two lines can be any of the following:
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yes
If no pair of lines is parallel and if each pairwise intersection is distinct, there will be 10 points of intersection.
If no pair of lines is parallel and if each pairwise intersection is distinct, there will be 6 points of intersection.
Six (6)
In Euclidian geometry it's a point. In non-Euclidean geometry all bets are off.