Equilateral triangle $$\triangle ABC$$ has centroid G. $$A_1$$, $$B_1$$, $$C_1$$ are points on $$\overline{AG}$$, $$\overline{BG}$$, $$\overline{CG}$$ such that $$\overleftrightarrow{A_1B_1}$$, $$\overleftrightarrow{B_1C_1}$$, $$\overleftrightarrow{C_1A_1}$$ are respectively parallel to $$\overleftrightarrow{AB}$$, $$\overleftrightarrow{BC}$$, $$\overleftrightarrow{CA}$$. If the distance between $$\overleftrightarrow{BC}$$ and $$\overleftrightarrow{B_1C_1}$$ is one-sixth of the altitude of $$\triangle ABC$$, determine the ratio of areas $$\frac{\triangle A_1B_1C_1}{\triangle ABC}$$.