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प्रश्न
ABCD is a quadrilateral. Find the sum the vectors \[\overrightarrow{BA} , \overrightarrow{BC} , \overrightarrow{CD}\] and \[\overrightarrow{DA}\]
उत्तर
Given: \[ABCD\] is a quadrilateral.
We need to find the sum of \[\overrightarrow{BA} + \overrightarrow{BC} + \overrightarrow{CD} + \overrightarrow{DA} .\]
Consider,
\[\overrightarrow{BA} + \overrightarrow{BC} + \overrightarrow{CD} + \overrightarrow{DA} \]
\[ = \left( \overrightarrow{BA} + \hspace{0.167em} \overrightarrow{DA} \right) + \left( \overrightarrow{BC} + \overrightarrow{CD} \right)\]
\[= \left( \overrightarrow{BD} + 2 \overrightarrow{DA} \right) + \overrightarrow{BD}\] [∵ \[\overrightarrow{BD} + \overrightarrow{DA} = \overrightarrow{BA}\] and \[\overrightarrow{BC} + \overrightarrow{CD} = \overrightarrow{BD}\]]
\[= 2 \left( \overrightarrow{BD} + \overrightarrow{DA} \right)\]
\[ = 2 \overrightarrow{BA}\]
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