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$\mathrm{ABCD}$ is a quadrilateral whose diagonals are $\mathrm{AC}$ and $\mathrm{BD}$. Which one of the following is correct?
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Verified Answer
The correct answer is:
$\overrightarrow{\mathrm{BA}}+\overrightarrow{\mathrm{CD}}=\overrightarrow{\mathrm{BD}}+\overline{\mathrm{CA}}$
$\overrightarrow{\mathrm{BA}}+\overrightarrow{\mathrm{AD}}=\overrightarrow{\mathrm{BD}}$...(i)
$\overrightarrow{\mathrm{CD}}+\overrightarrow{\mathrm{DA}}=\overrightarrow{\mathrm{CA}}$...(ii)
$(\mathrm{i})+(\mathrm{ii}) \Rightarrow \overrightarrow{\mathrm{BA}}+\overrightarrow{\mathrm{CD}}=\overrightarrow{\mathrm{BD}}+\overrightarrow{\mathrm{CA}}(\because \overrightarrow{\mathrm{AD}}, \overrightarrow{\mathrm{DA}}$ cancel $)$
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