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$\mathrm{ABCD}$ is a quadrilateral. Forces $\overrightarrow{\mathbf{A B}}, \overrightarrow{\mathbf{C B}}, \overrightarrow{\mathbf{C D}}$ and $\overrightarrow{\mathbf{D A}}$ act along its sides. What is their resultant?
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Verified Answer
The correct answer is:
$2 \overrightarrow{\mathbf{C B}}$
Let $\mathrm{ABCD}$ be a quadrilateral
$\overrightarrow{\mathrm{AB}}+\overrightarrow{\mathrm{CB}}+\overrightarrow{\mathrm{CD}}+\overrightarrow{\mathrm{DA}}$
$=\overrightarrow{\mathrm{AB}}+\overrightarrow{\mathrm{CB}}+\overrightarrow{\mathrm{CA}}(\because \overrightarrow{\mathrm{CD}}+\overrightarrow{\mathrm{DA}}=\overrightarrow{\mathrm{CA}})$
$=\overrightarrow{\mathrm{AB}}+\overrightarrow{\mathrm{CA}}+\overrightarrow{\mathrm{CB}}$
$=\overrightarrow{\mathrm{CB}}+\overrightarrow{\mathrm{CB}} \quad(\because \overrightarrow{\mathrm{AB}}+\overrightarrow{\mathrm{CA}}=\overrightarrow{\mathrm{CB}})$
$=2 \overline{\mathrm{CB}}$
$\overrightarrow{\mathrm{AB}}+\overrightarrow{\mathrm{CB}}+\overrightarrow{\mathrm{CD}}+\overrightarrow{\mathrm{DA}}$
$=\overrightarrow{\mathrm{AB}}+\overrightarrow{\mathrm{CB}}+\overrightarrow{\mathrm{CA}}(\because \overrightarrow{\mathrm{CD}}+\overrightarrow{\mathrm{DA}}=\overrightarrow{\mathrm{CA}})$
$=\overrightarrow{\mathrm{AB}}+\overrightarrow{\mathrm{CA}}+\overrightarrow{\mathrm{CB}}$
$=\overrightarrow{\mathrm{CB}}+\overrightarrow{\mathrm{CB}} \quad(\because \overrightarrow{\mathrm{AB}}+\overrightarrow{\mathrm{CA}}=\overrightarrow{\mathrm{CB}})$
$=2 \overline{\mathrm{CB}}$
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