Linear combination and a proof for the area.

http://dl.dropbox.com/u/25711584/algebra.jpg

$\displaystyle |DF|=3|AF|$

$\displaystyle |BE|=\frac{1}{2}|BC|$

* express $\displaystyle \bar{AG}$ as a linear combination of the vectors u=$\displaystyle \bar{AB}$ and v=$\displaystyle \bar{AD}$.

* Show that the triangle AFG always constitutes the same fraction of the area of the Parallelogram ABCD.

i need help here. On the first question i have tryed to express the vector AG with other vectors to finally come to an linear combination of u and v. But i get problems whit any vector that ends at G. I suppose i should use the symmetry of the triangles somehow but dont really know how?

the other question i need some tips to get started.

Thanks.