# Construction for Three Vectors with Sum Zero

Construction for Three Vectors with Sum Zero

On the sides of a triangle , construct three parallelograms , and . Then ++=0.

ABC

AEDB

BGFC

CHKA

⇀

DG

⇀

FH

⇀

KE

Proof: -+-+-=-+-+-=0.

⇀

BG

⇀

BD

⇀

CH

⇀

CF

⇀

AE

⇀

AK

⇀

BG

⇀

CF

⇀

CH

⇀

AK

⇀

AE

⇀

BD

You can move the vectors into a cyclic (sum-zero) configuration using the slider. Vertices can be moved with locators.