Let's remember that when using definite and indefinite articles that the noun is generally known or not known when an article is selected. "Where's Mary?" "She left with the vacuum cleaner. I guess that she's off cleaning a carpet somewhere." "She's upstairs cleaning the carpet in her bedroom."

Hello there! "Mary is cleaning THE carpet with A/THE vacuum cleaner" You can use A or THE vaccum cleaner, depending on if your'e talking about a specific vaccum cleaner. For example, "Mary is cleaning the carpet with THE vaccum cleaner that she used last night" Hope this helps!