Mathematics

Problem

\mathbf{a}

\mathbf{b}

and

\mathbf{c}

are three vectors such that

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

and

|\mathbf{a}| = 2

|\mathbf{b}| = 3

and

|\mathbf{c}| = 5

, then the value of

\mathbf{a} \cdot \mathbf{b} + \mathbf{b} \cdot \mathbf{c} + \mathbf{c} \cdot \mathbf{a}