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} $)
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 {AO} $
$2\overrightarrow {AO} $
$4\overrightarrow {AO} $
$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 $\overrightarrow{A O}=\overrightarrow{O D}$
$=6 \overrightarrow{A O}$
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