GATE Electronics and Communications (EC) 2020 Solved Papers

Given
For a uniform wave,
i.e., are mutually perpendicular to each other.
$(\overrightarrow{\mathit{k}}$ is the vector along the direction of wave propagation)
Comparing the given expression of $\overrightarrow{\mathit{H}}$ with the standard expression.
$\overrightarrow{\mathit{k}}=3{\mathit{a}}_{\mathit{x}}-{\mathit{a}}_{\mathit{y}}-{\mathit{a}}_{\mathit{z}}$
And, ${\overrightarrow{\mathit{H}}}_0=\left({\mathit{a}}_{\mathit{x}}+2{\mathit{a}}_{\mathit{y}}+\mathit{b}{\mathit{a}}_{\mathit{z}}\right)$
Then, $\overrightarrow{\mathit{k}}\cdot {\overrightarrow{\mathit{H}}}_0=3-2-\mathit{b}=0$
$\Rightarrow \mathit{b}=1$