Question

Five force $\overrightarrow{AB},\overrightarrow{AC},\overrightarrow{AD},\overrightarrow{AE},\overrightarrow{AF}$ act at the vertex $A$ of a regular hexagon $ABCDEF$. If $O$ is the centroid of the hexagon, then their resultant is a force given by

• A. $4\overrightarrow{AO}$
• B. $5\overrightarrow{AO}$
• C. $6\overrightarrow{AO}$
• D. None of these

Answer 1

Answer: (C)

$6\overrightarrow{AO}$

If $R$ is the resultant of given forces, then

$R=AB+AC+AD+AE+AF$

$=ED+AC+AD+AE+CD$ $[\because AB=ED$ and $AF=CD]$

$=(AC+CD)+(AE+ED)+AD$

$=AD+AD+AD=3AD=6AO$