What are its electron-pair and molecular geometries? what is the hybridization of the nitrogen atom? what orbitals on and overlap to form bonds between these elements?

electron-pair geometry =

molecular geometry =

hybridization =

the bonds are formed by the overlap of the hybrid orbitals on nitrogen with the orbitals .

Electron-pair geometry: tetrahedral

Molecular geometry: trigonal pyramidal

Hybridization: sp³

sp³ - 4 p

Explanation:

There is some info missing. I think this is the original question.

For NBr₃, What are its electron-pair and molecular geometries? What is the hybridization of the nitrogen atom? What orbitals on N and Br overlap to form bonds between these elements?

The N-Br bonds are formed by the overlap of the  ___ hybrid orbitals on nitrogen with ___ orbitals on Br.

Nitrogen is a central atom surrounded by 4 electron domains. According to VESPR, the corresponding electron-pair geometry is tetrahedral.

Of these 4 electron domains, 3 represent covalent bonds with Br and 1 lone pair. According to VESPR, the corresponding molecular geometry is trigonal pyramidal.

In the nitrogen atom, 1 s orbital and 3 p orbitals hybridize to form 4 sp³ orbitals for each of the electron domains.

The N-Br bonds are formed by the overlap of the sp³ hybrid orbitals on nitrogen with 4p orbitals on Br.

i believe you are right for all except the 3rd ( look at sqdancefan his answer is much better)