Nature of EM Waves & Wave Equation question from JEE Main 2015 (11 Apr, Shift 1)

Answer: (b)

1. Need $\vec{E}\cdot\vec{B} = 0$ and $\vec{E}\times\vec{B}$ along $+\hat{k}$. For in-plane vectors, the z-component of $\vec{E}\times\vec{B}$ is $E_xB_y - E_yB_x$.
2. (a): dot $= 0$, $z$-comp $= (1)(-1)-(2)(2) = -5$, along $-z$.
3. (b): dot $= -6+6 = 0$, $z$-comp $= (-2)(-2)-(-3)(3) = 13$, along $+z$.
4. (c): dot $= 8 \neq 0$. (d): dot $= 0$, $z$-comp $= -9-16 = -25$, along $-z$.
5. So the answer is (b).