In what kind of orbital do the lone-pair electrons on the nitrogen of dimethylacetamide reside, and is it in the same plane as the ch3 groups

The lone pairs on nitrogen in dimethylacetamide reside in sp3 orbitals which are coplanar with the methyl groups

Explanation:

The compound dimethylacetamide consists of oxygen bearing two lone pairs of electrons and a nitrogen atom bearing a lone pair of electrons and has two methyl groups attached to the nitrogen atom.

The lone pair on the nitrogen atom is accommodated in an sp3 orbital of nitrogen as shown in the question. This sp3 orbital is coplanar with the two methyl groups.