a. An electrostatic field line is a continuous curve. That is, a field line cannot have sudden breaks. Why not?
b. Explain why two field lines never cross each other at any point?

Explanation

Electric lines of force exist throughout the region of an electric field. The electric field of a charge decreases gradually with increasing distance from it and becomes zero at infinity i.e., electric field can.t vanish abruptly. So a line of force can.t have sudden breaks, it must be a continuous curve.
b. If two lines of force intersect, then there would be two tangents and hence two directions of electric fields at the point of interseetion, which is not possible.