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Triangle ABC is an equalateral triangle, with O it's centroid.

a) Show that vector OA + vector OB + vector OC = vector 0

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|OA|=|OB|=OC| symmetry
Add components in direction of OA
|OA| - |OB| sin 30 - |OC| sin 30
but sin 30=1/2

Add components perpendicular to OA
|OC|cos 30 - |OB| cos 30 = 0

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