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.

Can we conclude that does the whole state vote for both senators?
yes