Vector geometry, some problems.

[Gramsci]

I have two problems I need help with.

Homework Statement

ABCD is a parallellogram. E is the midpoint on BC. F is on AD so that |DF| = 8|AF|. G is the intersection between AE and BF.
a) Express the vector AG as a linear combination of u = AB and v = AD.
b) Show that the area of the triangle AFG always is the same fractional part of ABCD. Find that fractional part!

2.

Homework Equations

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The Attempt at a Solution

I have no idae. Any help would be nice.

 

[tiny-tim]

Hi Gramsci!

Do it step by step …

i] what is AE (in terms of u and v)?

ii] what is AF?

iii] so what is a general point on AE, and on BF?