Final answer:
Electric fields cannot cross each other because only a single electric-field line can exist at any given point, representing the sum of the electric fields from different charges at that point.
Step-by-step explanation:
The reason electric fields cannot cross each other is that at any given point in space, only a single electric field line can exist. Electric fields are the result of electrical charges, and these field lines are a visual representation of the electric force that would be exerted on a positive test charge placed at that point in the diagram. According to the principles of electric field maps and Maxwell's Equations, the electric field due to multiple charges is found by adding together the electric field from each individual charge to produce a resultant vector field. This means that the sum of the fields from different charges at a given point can only be a single resulting vector. Hence, electric-field lines cannot cross because such crossing would imply two different directions for the electric field at a single point, which is not possible.