The electric field vector of a wave is given as
\[
\overrightarrow{\mathrm{E}}=\mathrm{E}_{0} e^{t(\omega t +3x-4 y)} \frac{8 \vec{a}_{x}+6 \vec{a}_{y}+5 \vec{a}_{z}}{\sqrt{125}} \mathrm{~V} / \mathrm{m} .
\]
Its frequency is $10 \; \mathrm{GHz}$.
- Investigate if this wave is a plane wave.
- Determine its propagation constant, and
- Calculate the phase velocity in $y$-direction.