Question

If \[\vec{a}\], \[\vec{b}\], \[\vec{c}\] represent the sides of a triangle taken in order, then write the value of \[\vec{a} + \vec{b} + \vec{c} .\]

Answer 1

Let ABC  be a triangle such that \[\overrightarrow{BC} = \vec{a} , \overrightarrow{CA} = \vec{b}\] and \[\overrightarrow{AB} = \vec{c} .\] 
Then,
\[\vec{a} + \vec{b} + \vec{c} = \overrightarrow{BC} + \overrightarrow{CA} + \overrightarrow{AB}\] 
\[= \overrightarrow{BA} + \overrightarrow{AB} \]
\[ = \vec{0}\]                      [∵ \[\overrightarrow{BC} + \overrightarrow{CA} = \overrightarrow{BA}\]