For the circuit shown in Figure P7.39, we see that each voltage source has a phase difference of $2 \pi / 3$ in relation to the others.
a. Find $\overline{\mathbf{V}}_{E W}, \overline{\mathbf{V}}_{W E}$, and $\overline{\mathbf{V}}_{E R}$, where
$$
\begin{aligned}
& \overline{\mathbf{V}}_{\mathrm{F} W}=\tilde{\mathbf{V}}_{\mathrm{R}}-\tilde{\mathbf{V}}_{\mathrm{W}}, \overline{\mathbf{V}}_{\mathrm{WI}}=\overline{\mathbf{V}}_{\mathrm{W}}-\overline{\mathbf{V}}_{\mathrm{B}}, \text { and } \\
& \overline{\mathbf{V}}_{n R}=\overline{\mathbf{V}}_n-\hat{\mathbf{v}}_n \text {. }
\end{aligned}
$$
b. Repeat part a, using the calculations
$$
\begin{aligned}
& \overline{\mathbf{V}}_{R W}=\overrightarrow{\mathbf{V}}_R \sqrt{3} \angle-\pi / 6 \\
& \mathbf{V}_{W I}=\mathbf{V}_W \sqrt{3} \angle-\pi / 6 \\
& \mathbf{v}_{A R}=\mathrm{V}_{\mathrm{I}} \sqrt{3} \angle-\pi / 6
\end{aligned}
$$
c. Compare the results of part a with the results of part b.