Question

$\widehat{B} = \widehat{c} \times \widehat{E}$

$\Rightarrow \ \widehat{c} = \widehat{i}$ because phase of electric field is function of x .

$$\begin{matrix} \Rightarrow \ & \widehat{E} = \widehat{j}\text{~}\text{(given)}\text{~} \\ \Rightarrow \ & \widehat{B} = \widehat{i} \times \widehat{j} = \widehat{k} \\ & \ |\text{ }B| = \frac{|E|}{c} = \frac{69 \times 0.6 \times 10^{3}}{1.8 \times 10^{11}} = \frac{69}{3 \times 10^{8}} \\ & \ |\text{ }B| = 2.9 \times 10^{- 7} \\ & {\overrightarrow{\text{ }B}}_{2} = 2.9 \times 10^{- 7}sin\left( 0.6 \times 10^{3}x - 1.8 \times 10^{11}t \right) \end{matrix}$$

(phase is same as that of electric field)