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Question
If \[\vec{a}\], \[\vec{b}\], \[\vec{c}\] represent the sides of a triangle taken in order, then write the value of \[\vec{a} + \vec{b} + \vec{c} .\]
Solution
Let ABC be a triangle such that \[\overrightarrow{BC} = \vec{a} , \overrightarrow{CA} = \vec{b}\] and \[\overrightarrow{AB} = \vec{c} .\]
Then,
\[\vec{a} + \vec{b} + \vec{c} = \overrightarrow{BC} + \overrightarrow{CA} + \overrightarrow{AB}\]
\[= \overrightarrow{BA} + \overrightarrow{AB} \]
\[ = \vec{0}\] [∵ \[\overrightarrow{BC} + \overrightarrow{CA} = \overrightarrow{BA}\]
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