Question

If \[\vec{a}\], \[\vec{b}\], \[\vec{c}\] are position vectors of the vertices A, B and C respectively, of a triangle ABC, write the value of \[\overrightarrow{AB} + \overrightarrow{BC} + \overrightarrow{CA} .\]

Answer 1

Given: \[\vec{a} , \vec{b}\] and \[\vec{c}\] are the position vectors of A, B and C respectively.
Then,
\[\overrightarrow{AB} = \vec{b} - \vec{a} \]
\[ \overrightarrow{BC} = \vec{c} - \vec{b} \]
\[ \overrightarrow{CA} = \vec{a} - \vec{c} \]
Consider,
\[\overrightarrow{AB} + \overrightarrow{BC} + \overrightarrow{CA} = \vec{b} - \vec{a} + \vec{c} - \vec{b} + \vec{a} - \vec{c} \]
\[ = \vec{0}\]