Question: does the whole state vote for both senators

Answer: Yes, Elections to the Senate are held on the first Tuesday after the first Monday in November in even-numbered years, Election Day, and coincide with elections for the House of Representatives. Senators are elected by their state as a whole. The Elections Clause of the United States Constitution grants each state (and Congress, if it so desires to implement a uniform law) the power to legislate a method by which senators are elected. Ballot access rules for independent and minor party candidates also vary from state to state.