Question

Consider the regular hexagon $ABCDEF$ with centre at $O$ (origin).

Five forces $\overrightarrow{AB},\overrightarrow{AC},\overrightarrow{AD},\overrightarrow{AE},\overrightarrow{AF}$ act at the vertex $A$ of a regular hexagon $ABCDEF$, then their resultant is

• A. $3\overrightarrow{AO}$
• B. $2\overrightarrow{AO}$
• C. $4\overrightarrow{AO}$
• D. $6\overrightarrow{AO}$

Answer 1

The correct option is D $6\overrightarrow{AO}$

$\overrightarrow{R}=\overrightarrow{AB}+\overrightarrow{AC}+\overrightarrow{AC}+\overrightarrow{AE}+\overrightarrow{AF}$
$=\overrightarrow{ED}+\overrightarrow{AC}+\overrightarrow{AD}+\overrightarrow{AE}+\overrightarrow{CD}$
$(\because \overrightarrow{AB}=\overrightarrow{ED}$ and $\overrightarrow{AF}=\overrightarrow{CD})$
$=(\overrightarrow{AC}+\overrightarrow{CD})+(\overrightarrow{AE}+\overrightarrow{ED})+\overrightarrow{AD}$
$=\overrightarrow{AD}+\overrightarrow{AD}+\overrightarrow{AD}=3\overrightarrow{AD}=6\overrightarrow{AO}$