The lines of force can never intersect because they start from the positive charge and end on a negative charge. Hence they carry the same charge on them so they always repell each other. Secondly, on the line of force if we take a point and draw a tangent to it, it will give the direction of electric field at that point. So if the two lines intersect, that means at the same point two directions of electric fields is there which is just not possible.
