Explain Electric field intensity at any point due to a short Electric dipole?

Here short dipole is represented by AB. The moment of dipole is denoted by

It is along AB vector. The center of dipole is O. Now we have to find electric field intensity at point k.
According to the above mentioned data. OK=r

can be divided into two rectangular parts:

Let us represent KL along the direction of OK. Equation of field intensity at K on equitorial line.

Let us represent it with vector KM which is parallel to B₂A₂ and perpendicular to KL. Now complete the rectangle by joining the points MNKL. Now join KN.
By using the parallel law of vectors KN shows the resultant intensity E(vector) due to the dipole at point K.