Vector geometry, some problems.

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The discussion revolves around solving two vector geometry problems related to a parallelogram ABCD. The first problem involves expressing the vector AG as a linear combination of vectors u (AB) and v (AD). The second problem requires demonstrating that the area of triangle AFG is a consistent fractional part of the area of parallelogram ABCD and determining that fractional part. Participants suggest a step-by-step approach to find the necessary vectors and points. The conversation emphasizes breaking down the problems into manageable parts for clarity and understanding.
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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


-


The Attempt at a Solution


I have no idae. Any help would be nice.
 
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Hi Gramsci! :wink:

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? :smile:
 

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