# Math Help - vector

1. ## vector

ABCDEFGH is a regular octagon. State in terms of a single vector, the sum of the following vector
+AC+AF+AH+HG (sorry that I don't know how to type the arrows out..)
If | | =2, evaluate |AF| (vector too)

2. ## Re: vector

Hello, Trefoil2727!

$ABCDEFGH\text{ is a regular octagon. }\,\text{ State in terms of a single vector,}$
$\text{the sum of the following vector: }\:\overrightarrow{AB} + \overrightarrow{AC} + \overrightarrow{AF} + \overrightarrow{AH} + \overrightarrow{HG}$
Code:
              A       B
o-------o
/|  *     \
/ |     *   \
/  |        * \
H o   |           o C
|   |           |
|   |           |
|   |           |
G o   |           o D
\ *|          /
\ | *       /
\|    *   /
o-------o
F       E
Note that: . $\overrightarrow{AC} \,=\,\overrightarrow{GE},\;\overrightarrow{AB} \,=\,\overrightarrow{FE}$

We have: . $\overrightarrow{AB} + \overrightarrow{AC} + \overrightarrow{AF} + \overrightarrow{AH} + \overrightarrow{HG}$

. . . . . . $=\;\left(\overrightarrow{AH} + \overrightarrow{HG} + \overrightarrow{AC}\right) + \left(\overrightarrow{AF} + \overrightarrow{AB}\right)$

. . . . . . $=\;\left(\overrightarrow{AH} + \overrightarrow{HG} + \overrightarrow{GE}\right) + \left(\overrightarrow{AF} + \overrightarrow{FE}\right)$

. . . . . . $=\;\overrightarrow{AE} + \overrightarrow{AE}$

. . . . . . $=\; 2\overrightarrow{AE}$

$\text{If }|\overrightarrow{AB}| = 2,\,\text{ evaluate }|\overrightarrow{AF}|.$

$\text{If the side of the octagon is }|\overrightarrow{AB}| = 2$
. . $\text{then }|\overrightarrow{AF}|\text{ is the side of the circumscribing square.}$

Code:
              A   2   B
* - o-------o - *
_ :  /|        \  :
√2 : /2|        2\ :
:/  |          \:
o   |           o
|   |           |
2|   |           |2
|   |           |
o   |           o
_ :\  |          /:
√2 : \2|        2/ :
:  \|        /  :
* - o-------o - *
F   2   E
We see that: . $|\overrightarrow{AF}| \:=\:2+2\sqrt{2}$