GATE Electronics and Communications (EC) 2016 Shift 1 Solved Paper

The electric field of a uniform plane wave traveling along the negative z-direction is given by the following equation:
${\overrightarrow{\mathit{E}}}_{\mathit{w}}^{\mathit{i}}=\left({\hat{\mathit{a}}}_{\mathit{x}}+\mathit{j}{\hat{\mathit{a}}}_{\mathit{y}}\right){\mathit{E}}_0{\mathit{e}}^{\mathit{j}\mathit{k}\mathit{z}}$
This wave is incident upon a receiving antenna placed at the origin and whose radiated electric field towards the incident wave is given by the following equation:
${\overrightarrow{\mathit{E}}}_{\mathit{a}}^{\mathit{i}}=\left({\hat{\mathit{a}}}_{\mathit{x}}+2{\hat{\mathit{a}}}_{\mathit{y}}\right){\mathit{E}}_{\mathit{I}}\frac{1}{\mathit{r}}{\mathit{e}}^{-\mathit{j}\mathit{k}\mathit{r}}$
The polarization of the incident wave, the polarization of the antenna, and losses due to the polarization mismatch are, respectively,