Vector geometry, some problems.

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SUMMARY

The discussion focuses on solving vector geometry problems involving a parallelogram ABCD, where E is the midpoint of BC and F is positioned on AD such that |DF| = 8|AF|. The primary tasks are to express vector AG as a linear combination of vectors u = AB and v = AD, and to demonstrate that the area of triangle AFG is a consistent fractional part of the area of parallelogram ABCD. The solution requires a step-by-step approach to determine vectors AE and AF, leading to the calculation of the area ratio.

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Gramsci
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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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