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1. Dot product in a regular tetrahedron ●●●○○ 50 ptsGiven a regular tetrahedron $P-ABC$ with edge length $1$, points $E, F, G, H$ lie on edges $PA, PB, CA, CB$ respectively. If $\overrightarrow{EF}+\overrightarrow{GH}=\overrightarrow{AB}$ and $\overrightarrow{EH} \cdot \overrightarrow{FG}=\frac{1}{18}$, find $\overrightarrow{EG} \cdot \overrightarrow{FH}$. Round to two decimal places.