A point electric dipole of moment ${\overrightarrow{\mathrm{p}}}_1=(\sqrt{3} \hat{\mathrm{i}}+\hat{\mathrm{j}})$ is held fixed at the origin. Another point electric dipole of moment ${\overrightarrow{\mathrm{P}}}_2$ held at the point A(+a, 0, 0) will have minimum potential energy, if its orientation 

For minimum P.E. on $\overrightarrow{\mathrm{p}}$ it should be held along the direction of electric field at that point:

$\begin{array}{l}{\mathrm{E}}_{\text{axail }}=\frac{+2\mathrm{k}\left(\sqrt{3}\mathrm{P}\right)}{{\mathrm{a}}^3}\\ {\mathrm{E}}_{\text{equi }}=\frac{\mathrm{kP}}{{\mathrm{a}}^3}\end{array}$

$\mathrm{\theta }={\tan }^{-1}\left(\frac{{\mathrm{E}}_{\text{equi }}}{{\mathrm{E}}_{\text{axial }}}\right)=\frac{\frac{\mathrm{kP}}{{\mathrm{a}}^3}}{\frac{2\mathrm{k}\sqrt{3}\mathrm{P}}{{\mathrm{a}}^3}}={\tan }^{-1}(-1/2\sqrt{3})$

E_equi is ‘-ve’ due to opposite direction of P;

$\therefore$direction of dipole $2\sqrt{3} \hat{\mathrm{i}}-\hat{\mathrm{j}}$