Electrical – How to calculate the voltage across Va and Vb

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.

Yes your answer is correct.

I would however have shown the equations for finding the first two voltages. In a test the method usually gets you more marks than the value.

BTW: There are almost always more than one way to solve these kinds of problems. As such, it is prudent, and a good habit to get into, to do so to verify your work.

In this example. you know

\$R_{TOTAL} = (V_S-V_d)/I_D = (20-2.1)/0.0075 = 2386.67\Omega\$

So

\$R_3 = 2386.67 - 1100 - 450 = 836.67\Omega\$

Addition: Since the assignment also asks you to verify KVL, it may be prudent to work your answer the other way around. Using KVL as part of your initial math method does not "prove" it per se.

So finding R3 from the above, then calculating the voltages across reach resistor to show that \$V_{R1} + V_{R2} + V_{R3} + V_D = V_S\$ would be a better way to answer it.