Calculate op-amp output voltage
As you said, $$V_a = V_b = V_{in}$$
As \$V_{in}=V_a\$, there is no current through \$R_1\$. Since there is no current flowing into/from the negative terminal as well, we conclude that there is no current through \$R_2\$ as well. So if there is no current through \$R_2\$, the voltage on both sides of it is equal, and it is \$V_a\$ which is \$V_{in}\$. So \$V_{out}=V_{in}\$ as expected. No currents through resistors.