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(A) In an equilateral triangle $ABC$,the centroid $O$ is the point where the medians intersect. Since the triangle is equilateral,the vectors $\overri

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$0$

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(A) In an equilateral triangle $ABC$,the centroid $O$ is the point where the medians intersect. Since the triangle is equilateral,the vectors $\overrightarrow{OA}$,$\overrightarrow{OB}$,and $\overrightarrow{OC}$ have equal magnitudes and are directed from the centroid to the vertices. The angles between these vectors are $120^{\circ}$ each. According to the principle of vector addition for symmetric systems,the resultant of three vectors of equal magnitude separated by $120^{\circ}$ is zero. Therefore,$\overrightarrow{OA} + \overrightarrow{OB} + \overrightarrow{OC} = \vec{0}$.

$ABC$ is an equilateral triangle. The length of each side is $a$ and the centroid is point $O$. Then $\overrightarrow{OA} + \overrightarrow{OB} + \overrightarrow{OC} = \dots$

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