ABCDEF is a regular hexagon. Find the sum of | vedclass

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(D) Let the center of the regular hexagon $ABCDEF$ be the origin $O$.We express each vector in terms of the position vectors of the vertices relative

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$3\vec{BF}$

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(D) Let the center of the regular hexagon $ABCDEF$ be the origin $O$.We express each vector in terms of the position vectors of the vertices relative to the origin $O$.$\vec{BE} + \vec{BC} + \vec{EF} + \vec{BA} + \vec{CF} + \vec{AF}$$= (\vec{OE} - \vec{OB}) + (\vec{OC} - \vec{OB}) + (\vec{OF} - \vec{OE}) + (\vec{OA} - \vec{OB}) + (\vec{OF} - \vec{OC}) + (\vec{OF} - \vec{OA})$Grouping the terms,we observe that $\vec{OE} - \vec{OE} = 0$,$\vec{OC} - \vec{OC} = 0$,and $\vec{OA} - \vec{OA} = 0$.This simplifies to: $3\vec{OF} - 3\vec{OB}$$= 3(\vec{OF} - \vec{OB})$$= 3\vec{BF}$.

$ABCDEF$ is a regular hexagon. Find the sum of the vectors $\vec{BE} + \vec{BC} + \vec{EF} + \vec{BA} + \vec{CF} + \vec{AF}$.

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