The type of hybridization of boron and oxygen atom in boric acid $\left({\mathrm{H}}_3{\mathrm{BO}}_3\right)$ are respectively

B has ${\mathrm{sp}}^2$ and oxygen has ${\mathrm{sp}}^3\mathrm{hybridization}$.

Boric acid $\mathrm{HO}-\stackrel{\underset{|}{\mathrm{OH}}}{\mathrm{B}}-\mathrm{OH}$; has a network structure in which boron is trigonal having  sp²  and each oxygen atom is tetrahedral having  sp³ - hybridization with two lone pair of electrons on oxygen.