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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.
Option: 1 \frac{1}{\sqrt{2}}\left ( \hat{j}+\hat{k} \right )
 
Option: 2 \frac{1}{\sqrt{5}}\left ( 2\hat{i}+\hat{j} \right )
Option: 3 \frac{1}{\sqrt{5}}\left ( \hat{i}+2\hat{j} \right )  
Option: 4 \frac{1}{\sqrt{2}}\left ( \hat{i}+\hat{j} \right )

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\begin{array}{l} As \ \ \overrightarrow{\mathrm{E}} \times \overrightarrow{\mathrm{B}} \ \ \| \ \overrightarrow{\mathrm{C}} \\ \hat{\mathrm{E}} \times \hat{\mathrm{B}}=\frac{1}{\sqrt{2}}\left|\begin{array}{ccc} \hat{\mathrm{i}} & \hat{\mathrm{j}} & \hat{\mathrm{k}} \\ 0 & 0 & 1 \\ 1 & -1 & 0 \end{array}\right|=\frac{\hat{\mathrm{i}}+\hat{\mathrm{j}}}{\sqrt{2}} \quad \\ \Rightarrow \hat{\mathrm{C}}=\frac{\hat{\mathrm{i}}+\hat{\mathrm{j}}}{\sqrt{2}} \end{array}

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