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

1 Answer
Mar 14, 2018

That's true

Explanation:

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

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

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