In a plane electromagnetic wave, the directions of electric field and magnetic field are represented by \(\hat{ k }\) and \(2 \hat{ i }-2 \hat{ j },\) respectively What is the unit vector along direction of propagation of the wave.

\(\overrightarrow{ B }=2 \hat{ i }-2 \hat{ j } \Rightarrow \hat{ B }=\frac{\overrightarrow{ B }}{| B |}=\frac{2 \hat{ i }-2 \hat{ j }}{2 \sqrt{2}}\)

\(\Rightarrow \hat{ B }=\frac{1}{\sqrt{2}}(\hat{ i }-\hat{j})\)

Direction of wave propagation \(=\hat{ C }=\hat{ E } \times \hat{ B }\)

\(\hat{ C }=\hat{ k } \times\left[\frac{1}{\sqrt{2}}(\hat{ i }-\hat{ j })\right]\)

\(\hat{ C }=\frac{1}{\sqrt{2}}(\hat{ k } \times \hat{ i }-\hat{ k } \times \hat{ j })\)

\(\hat{ C }=\frac{1}{\sqrt{2}}(\hat{ i }+\hat{ j })\)