Figure shows ABCDEF as a regular hexagon.

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Figure shows $ABCDEF$ as a regular hexagon. What is the value of $\overrightarrow {AB} + \overrightarrow {AC} + \overrightarrow {AD} + \overrightarrow {AE} + \overrightarrow {AF} $ (in $\overrightarrow {AO} $)

A

$\overrightarrow {AO} $

B

$2\overrightarrow {AO} $

C

$4\overrightarrow {AO} $

D

$6\overrightarrow {AO} $

Figure shows $ABCDEF$ as a regular hexagon. What is the value of $\overrightarrow {AB} + \overrightarrow {AC} + \overrightarrow {AD} + \overrightarrow {AE} + \overrightarrow {AF} $ (in $\overrightarrow {AO} $)

$\overrightarrow{A B}+\overrightarrow{A C}+\overrightarrow{A D}+\overrightarrow{A E}+\overrightarrow{A F}$

$=\overrightarrow{A B}+(\overrightarrow{A C}+\overrightarrow{A F})+\overrightarrow{A D}$$+\overrightarrow{A E}$

$=\overrightarrow{A B}+(\overrightarrow{A C}+\overrightarrow{C D})+\overrightarrow{A D}$

$+\overrightarrow{A E}[\sin c e \overrightarrow{A F}=\overrightarrow{C D}]$

$=\overrightarrow{A B}+\overrightarrow{A D}+\overrightarrow{A D}+\overrightarrow{A E}$

$=2 \overrightarrow{A D}+(\overrightarrow{A B}+\overrightarrow{A E})$

$=2 \overrightarrow{A D}+(\overrightarrow{E D}+\overrightarrow{A E})$

$[\sin c e \overrightarrow{A B}=\overrightarrow{E D}$

$=2 \overrightarrow{A D}+\overrightarrow{A D}$

$=3 \overrightarrow{A D}$

$=3 (2 \overrightarrow{A O}) \quad[\text { since } O$ is the center

and $\overrightarrow{A O}=\overrightarrow{O D}$

$=6 \overrightarrow{A O}$