GO:0003827:   alpha-1,3-mannosylglycoprotein 2-beta-N-acetylglucosaminyltransferase activity
Catalysis of the reaction: 3-(alpha-D-mannosyl)-beta-D-mannosyl-R + UDP-N-acetyl-alpha-D-glucosamine = 3-(2-[N-acetyl-beta-D-glucosaminyl]-alpha-D-mannosyl)-beta-D-mannosyl-R + H(+) + UDP.