the vp of the senate
The Senate is where the VP presides.
The Senate President Pro Tempore
The President of the Senate (VP of US) votes to break ties.
The VP of the US chairs the Senate.
The VP chairs the Senate and can vote if a tie-vote occurs. Therefore the party that the VP belongs to can pass legislation with only 50 votes.
He is the VP and not a voting member of the Senate, but he can vote in the event of a tie.
The VP is not a Senator. His job is to chair meetings. He can not vote unless there is a tie vote.
VP Joe Biden
majority leader
There is no Vice-president in that case. That office remains vacant and the duties of the Vice-president to preside over the Senate is then handled by the President pro tempore of the Senate.
John Adams, because he was the first president of the Senate -- he was VP, and the VP casts the tiebreaker vote.
VP Joe Biden serve 30 years in the Senate or 5 full terms. He was elected to a 6th consecutive Senate term but could not accept it because he elected as VP at the same time.