Before we go much farther we have to get on the same page with terms.
Sink= kitchen sink. Lavatory= bathroom sink.
The vent will come off top of the sanitary tee used to stub out for the lavatory and will run a vent out the roof or revent back into a dry vent in the attic. If you have two lavatories,( and you only mention it by adding a "s" onto sink.) they will connect by a continuous waste, drain into the same tee and be vented by the same vent.
More terms, Stack vent= a vent that has fixtures draining into it. Vent stack= a stack vent that's above all the fixtures that drain inti it and runs out the roof.
You may revent into the vent stack at any point over 6" above the flood rim of the highest fixture draining into it.
Sorry for the technical terms but I'm a plumber and that's how we make ourselves understood. Regards, Tom
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