ABCD is a quadrilateral. Show that vec(AB)+vec(AD)+vec(CB)+vec(CD)=4vec(PQ)−−→AB+−−→AD+−−→CB+−−→CD=4−−→PQ where P and Q are the mid points of AC and BD respectively?

1 Answer
Zsigmond S.
Mar 14, 2018

That's true

Explanation:

https://www.geogebra.org/m/WgaNJ5Xq

enter image source here

\vec (AB)+\vec (AD)= 2 \cdot \vec (AQ)−−→AB+−−→AD=2⋅−−→AQ
\vec (AB)+\vec (BC)= 2 \cdot \vec (AP)−−→AB+−−→BC=2⋅−−→AP
\vec (PQ)=\vec (AQ)- \vec (AP)−−→PQ=−−→AQ−−−→AP

2 cdot \vec(PQ)=\vec (AD)+\vec(CB)2⋅−−→PQ=−−→AD+−−→CB
2 cdot \vec(PQ)=\vec (AB)+\vec(CD)2⋅−−→PQ=−−→AB+−−→CD

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