Answer :

mashenka
They cannot cross because they have different values. Each line has its own value and if they could cross, that would mean that we can have 2 different values at the same point (and it cannot be true).
AL2006
Electric field 'lines' were invented by people, to have a visualization of the
electric field.  We draw 'lines' to show the direction of the force that a tiny
test charge would feel if it were at any point in the field, and the direction
it would move from there. 

If 'lines' crossed, then there would be a point in the field where a tiny test
charge would feel a force in two different directions, and it would have a
choice of which way to go from there.  That doesn't happen.

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