In a plane electromagnetic wave, the directions of electric field and magnetic field are represented
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.
Correct Option: 1
$\hat{\mathrm{E}}=\hat{\mathrm{k}}$
$\overrightarrow{\mathrm{B}}=2 \hat{\mathrm{i}}-2 \hat{\mathrm{j}} \Rightarrow \hat{\mathrm{B}}=\frac{\overrightarrow{\mathrm{B}}}{|\mathrm{B}|}=\frac{2 \hat{\mathrm{i}}-2 \hat{\mathrm{j}}}{2 \sqrt{2}}$
$\Rightarrow \hat{\mathrm{B}}=\frac{1}{\sqrt{2}}(\hat{\mathrm{i}}-\hat{\mathrm{j}})$
Direction of wave propagation $=\hat{\mathrm{C}}=\hat{\mathrm{E}} \times \hat{\mathrm{B}}$
$\hat{\mathrm{C}}=\hat{\mathrm{k}} \times\left[\frac{1}{\sqrt{2}}(\hat{\mathrm{i}}-\hat{\mathrm{j}})\right]$
$\hat{\mathrm{C}}=\frac{1}{\sqrt{2}}(\hat{\mathrm{k}} \times \hat{\mathrm{i}}-\hat{\mathrm{k}} \times \hat{\mathrm{j}})$
$\hat{\mathrm{C}}=\frac{1}{\sqrt{2}}(\hat{\mathrm{i}}+\hat{\mathrm{j}})$