Mathematics

Problem

\vec{a}

\vec{b}

and

\vec{c}

are three vectors such that

|\vec{a}| = 5

|\vec{b}| = 12

|\vec{c}| = 13

and

\vec{a} + \vec{b} + \vec{c} = \vec{0}

, find the value of

(\vec{a} \cdot \vec{b} + \vec{b} \cdot \vec{c} + \vec{c} \cdot \vec{a})

. [CBSE 2012]