A surface of area $\vec A = 2\hat i - 3\hat k$ exists is a region of electric field $\vec E = a\hat i + b\hat j$. The net flux passing through the surface is

$2a$

The correct answer is Option (3) → $2a$

Flux $\Phi = \vec{E} \cdot \vec{A}$

$\vec{E} = a\hat{i} + b\hat{j}$

$\vec{A} = 2\hat{i} - 3\hat{k}$

$\Phi = (a\hat{i} + b\hat{j}) \cdot (2\hat{i} - 3\hat{k})$

$= 2a + 0 + 0 = 2a$

Answer: $2a$