Correct answer is (a)
We know that propagation wave vector
∵ \(\vec{E} = \hat{k}\)
\(\vec{B} = 2\hat{i} - 2\hat{j}\)
\(\vec{C} = \vec{E} \times \vec{B}\)
\(\vec{C} = \begin{vmatrix}
\hat{i} & \hat{j} & \hat{k} \\
0 & 0 & 1 \\
2 & -2 & 0
\end{vmatrix}\)
\(\vec{C} = \hat{i}(0 + 2) - \hat{j}(0 - 2) + 0\,\hat{k}\)
\(\vec{C} = 2\hat{i} + 2\hat{j}\)
unit vector of propagation wave = \(\frac{\vec{C}}{|\vec{C}|}\)
\(=\frac{2\hat{i} + 2\hat{j}}{\sqrt{4 + 4}}\)
\(=\frac{2\hat{i} + 2\hat{j}}{\sqrt{8}}\)
\(\Rightarrow \frac{1}{\sqrt{2}}(\hat{i} + \hat{j})\)