No. If they did, that would mean that at the point of intersection, the force field points in two different directions simultaneously!
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No, horizontal lines are parallel to each other and parallel lines never intersect.
Lines that that intersect each other at right angles on a plane are perpendicular lines.
Perpendicular lines intersect at right angles to each other.
Lines which are parallel. All other lines on the same plane eventually intersect.
the parallel lines never intersect each other but they both intersect the line they are perpendicular to