ABCDE is a pentagon. Forces AB , ,AE , ,DC , ,ED act at a point. … - Vidyadip

MCQ

$ABCDE$ is a pentagon. Forces $\overrightarrow {AB} ,\,\overrightarrow {AE} ,\,\overrightarrow {DC} ,\,\overrightarrow {ED} $ act at a point. Which force should be added to this system to make the resultant $ 2 \overrightarrow {AC} $

A
$\overrightarrow {AC} $
B
$\overrightarrow {AD} $
✓
$\overrightarrow {BC} $
D
$\overrightarrow {BD} $

✓

Answer

Correct option: C.

$\overrightarrow {BC} $

c
(c) $\overrightarrow {AE} + \overrightarrow {ED} + \overrightarrow {DC} + \overrightarrow {AB} = \overrightarrow {AD} + \overrightarrow {DC} + \overrightarrow {AB} $$ = \overrightarrow {AC} + \overrightarrow {AB} .$

Obviously, if $\overrightarrow {BC} $ is added to this system, then it will be $\overrightarrow {AC} + \overrightarrow {AB} + \overrightarrow {BC} = \overrightarrow {AC} + \overrightarrow {AC} = 2\overrightarrow {AC} .$

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