(a) Current does not add according to the vector (parallelogram) law — at a junction, currents simply add algebraically (Kirchhoff's current law), regardless of the angle of the wires. The arrow drawn merely indicates the assumed conventional sense of flow, not a true vector direction. Hence current is treated as a scalar (signed) quantity, not a vector.

(b) Wheatstone bridge balance condition: consider arms $P$, $Q$, $R$, $S$ with a galvanometer across the bridge and a cell driving current through the network. At balance, no current flows through the galvanometer, so the same current $I_1$ flows through $P$ and $Q$, and the same current $I_2$ flows through $R$ and $S$. Also, since no current flows through the galvanometer, the potential at both ends of the galvanometer arm are equal:

$$I_1P=I_2R \quad \text{and} \quad I_1Q=I_2S$$

Dividing these:

$$\frac{P}{Q}=\frac{R}{S}$$

This is the balance condition of the Wheatstone bridge.