Consider an electric dipole consisting of charges $-q$ and $+q$, separated by a distance $2a$ and placed in free space. Let $P$ be point on the line joining the two charges (axial line) at a distance $r$ from the centre of $O$ of the dipole.
You can observe in the above figure that electric field has two directions at the same point $P$, does this mean electric field lines of two charges can intersect?
This is the common figure given in all text books, what I can observe is that field line due to $+q$ charge ends at $-q$ charge and then it doesn't progress towards the point $P$, and nowhere I see the lines of $+q$ and $-q$ intersecting, now I can't conclude that field lines do intersect. So, does field line concept explain electric field due to electric dipole?
What I observed in Wikipedia dipole page is that, axial line is only vanishing!
Sometimes I might have misunderstood the concept, if so pardon me and explain.