Question

Two forces act at the vertex $A$ of a quadrilateral $ABCD$ represented by $\overrightarrow{AB},\overrightarrow{AD}$ and two at $C$ represented by $\overrightarrow{CB}$ & $\overrightarrow{CD}$. If $E$ and $F$ are the middle points of $AC$ and $BD$ respectively, then the resultant of all forces is represented by

• A. $\overrightarrow{EF}$
• B. $2\overrightarrow{EF}$
• C. $\frac{3}{2}\overrightarrow{EF}$
• D. none of these

Answer 1

The correct option is D none of these

We have,

$AB+AD=2AF,$ where $F$ is mid-point of $BD$

Also, $CB+CD=2CF;$

$\therefore AB+AD+CB+CD$

$=2(AF+CF)=-2(FA+FC)=-2\left[2FE\right],$

where $E$ is the mid=point of $AC=-4FE=4EF.$