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(A) The direction of propagation of an electromagnetic wave is given by the direction of the Poynting vector,which is $\hat{E} 	imes \hat{B}$.Given,t

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

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(A) The direction of propagation of an electromagnetic wave is given by the direction of the Poynting vector,which is $\hat{E} 	imes \hat{B}$.Given,the direction of the electric field is $\hat{E} = \hat{k}$.The direction of the magnetic field is given by the vector $\vec{B} = 2\hat{i} - 2\hat{j}$.The unit vector for the magnetic field is $\hat{B} = \frac{\vec{B}}{|B|} = \frac{2\hat{i} - 2\hat{j}}{\sqrt{2^2 + (-2)^2}} = \frac{2\hat{i} - 2\hat{j}}{\sqrt{8}} = \frac{2\hat{i} - 2\hat{j}}{2\sqrt{2}} = \frac{1}{\sqrt{2}}(\hat{i} - \hat{j})$.The direction of propagation $\hat{C}$ is $\hat{E} 	imes \hat{B} = \hat{k} 	imes [\frac{1}{\sqrt{2}}(\hat{i} - \hat{j})]$.Using the cross product rules $\hat{k} 	imes \hat{i} = \hat{j}$ and $\hat{k} 	imes \hat{j} = -\hat{i}$,we get:$\hat{C} = \frac{1}{\sqrt{2}}(\hat{k} 	imes \hat{i} - \hat{k} 	imes \hat{j}) = \frac{1}{\sqrt{2}}(\hat{j} - (-\hat{i})) = \frac{1}{\sqrt{2}}(\hat{i} + \hat{j})$.

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

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