For the given circuit, calculate
\sum_{k=1}^3 v_x i_x
From the circuit, we have
\begin{aligned} \sum_{k=1}^3 v_x i_x & =v_1 i_1+v_2 i_2+v_3 i_3=-20 \times 3+15 \times 3+5 \times 3 \\ & =-60+45+15=0 W \end{aligned}