Nature of EM Waves & Wave Equation question from JEE Main 2019 (10 Jan, Shift 2)

Answer: (b)

1. $\vec{k} = 6\hat{i} + 8\hat{k}$, $|\vec{k}| = 10$, so $\omega = c|\vec{k}| = 10c$ and phase is $(6x + 8z - 10ct)$.
2. $\vec{B} = \dfrac{1}{c}\,\hat{n} \times \vec{E}$ with $\hat{n} = \dfrac{6\hat{i} + 8\hat{k}}{10}$, $\vec{E} = 10\hat{j}$.
3. $\hat{n} \times 10\hat{j} = 6(\hat{i} \times \hat{j}) + 8(\hat{k} \times \hat{j}) = 6\hat{k} - 8\hat{i}$.
4. So the answer is (b) $\dfrac{1}{c}(6\hat{k} - 8\hat{i})\cos(6x + 8z - 10ct)$.