MCQ
$ABCDEF$ is a regular hexagon and forces represented in magnitude and direction by $AB, AC,AD, AE$ and $AF$ act at $A$. Their resultant is :
- A$6\, AD$
- B$4\, AD$
- ✓$3\, AD$
- D$2\, AD$
✓
Answer
Correct option: C.
$3\, AD$
c
$\overrightarrow{\mathrm{AB}}+\overrightarrow{\mathrm{AC}}+\overrightarrow{\mathrm{AD}}+\overrightarrow{\mathrm{AE}}+\overrightarrow{\mathrm{AF}}$
$\overrightarrow{\mathrm{AB}}+\overrightarrow{\mathrm{AC}}+\overrightarrow{\mathrm{AD}}+\overrightarrow{\mathrm{AE}}+\overrightarrow{\mathrm{AF}}$
$=(\overrightarrow{\mathrm{AB}}+\overrightarrow{\mathrm{AE}})+(\overrightarrow{\mathrm{AC}}+\overrightarrow{\mathrm{AF}})+\overrightarrow{\mathrm{AD}}$
$=\overrightarrow{\mathrm{AD}}+\overrightarrow{\mathrm{AD}}+\overrightarrow{\mathrm{AD}}=3 \overrightarrow{\mathrm{AD}}$
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