why two lines of force never intersect each other?

this is because at a point of intersection, we can draw two tangents to the two lines of force .this would mean two directions of electric field intensity at the point of interesection, which is not possible.

Consider two lines of force will intersect each other. Then draw the tangents to find the direction of the force. There will be two directions. This is not possible So the lines of force never intersect each other.