Electric Field Intensity due to an infinitely long straight uniformly charged wire 
This the photo of my textbook, Here In the derivation of Electric Field Intensity due to an infinitely long straight uniformly charged wire -
In the figure 1(c).20 Vector E1 and vector E2 are electric fields at point P due to the two line elements as shown in the figure 1(c).20.
But, in this figure 1(c).20 two Electric field lines are shown intersecting PE1 and PE2, how can this be done as we know that Two electric field lines never intersect each other then how are they intersecting here....
If anyone wants to know what electric field lines are you can go here-
https://byjus.com/physics/electric-field-lines/
please help me.....
 A: The arrows in the diagram are not real electric field lines, but rather the contribution to the electric field given by the infinitesimal line elements PE1 and PE2. These can certainly intersect.
Electric field lines are something totally different from what is shown in the figure. For the infinite line coming out of the page it would look like:

It is true that two electric field lines never intersect, and indeed if one drew the electric field lines for the distribution they would point radially outwards, no intersection as needed.
A: They are showing electric field lines due to individual charge segments at different locations along the wire, not the net electric field due to the whole wire.
A: What is meant with that picture is simply that the electric field lines $E_1$ and $E_2$ that the individual positive charged particles $P_1$ and $P_2$ create (representing each electric fieldline from each charged particle of the charged surface) cancel each other out tangentially. This results in an overall electric field $E$ that is orthogonal to the positive charged surface. The fact that fieldlines don't overlap each other only applies to this overall electric field, as the idea behind it, is the overall electric field being unique in every point in space.
A: That's a terrible illustration.
Those lines are neither field lines nor vectors.  Those lines having arrows at the end don't represent anything.   I will give the author the benefit of the doubt and suppose that he or she intended to display vectors anchored at the point of interest.  The lines below the dotted line are perhaps to display the length and direction of the field point with respect to the charge element.   The two should be differentiated somehow, perhaps by making one a dotted line, or a different color line.
