Equipotentials cannot cross because they relate to places with a given value for potential. Lines of force meet at the charge or point of mass.
They can cross if they relate to the same potential. Think of two mountain chains of unvarying height crossing each-other.
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If the field lines were not perpendicular to the surface, then they could be decomposed into components perpendicular and parallel to the surface. But if there is an E-field along the surface, the surface is no longer an equipotential.
Two lines cross at a point.
intersecting lines...
The lines that cross at a 90 degree angle are called Perpindicular lines.
Two lines cross or intersect at a point.