Question

a) write ao in terms of $\boldsymbol{p}$ and/or $\boldsymbol{q}$.b) write $overrightarrow{ob}$ in terms of $\boldsymbol{p}$ and/or $\boldsymbol{q}$.c) write $overrightarrow{eb}$ in terms of $\boldsymbol{p}$ and/or $\boldsymbol{q}$.give each answer in its simplest form.not drawn accurately

Explanation:

Step1: Recognize hexagon property

In a regular hexagon, the vector from the center to a vertex is equal and parallel to the vector of the opposite side. So $\overrightarrow{AO} = \overrightarrow{BC}$.
$\overrightarrow{AO} = 5\boldsymbol{p}$

Step2: Find $\overrightarrow{OB}$ using vector addition

$\overrightarrow{OB} = \overrightarrow{OA} + \overrightarrow{AB}$, and $\overrightarrow{OA} = -\overrightarrow{AO}$.
$\overrightarrow{OB} = -5\boldsymbol{p} + (4\boldsymbol{p} + \boldsymbol{q}) = -5\boldsymbol{p} + 4\boldsymbol{p} + \boldsymbol{q} = -\boldsymbol{p} + \boldsymbol{q}$

Step3: Find $\overrightarrow{EB}$ using hexagon symmetry

In a regular hexagon, $\overrightarrow{EB} = \overrightarrow{AO} + \overrightarrow{AB}$.
$\overrightarrow{EB} = 5\boldsymbol{p} + (4\boldsymbol{p} + \boldsymbol{q}) = 5\boldsymbol{p} + 4\boldsymbol{p} + \boldsymbol{q} = 9\boldsymbol{p} + \boldsymbol{q}$

Answer:

a) $\boldsymbol{5p}$
b) $\boldsymbol{-p + q}$
c) $\boldsymbol{9p + q}$