Mathematics

Problem

Let

\boldsymbol{a}, \boldsymbol{b}, \boldsymbol{c}

are three vectors of which every pair is non-collinear. If the vectors

\boldsymbol{a} + \boldsymbol{b}

and

\boldsymbol{b} + \boldsymbol{c}

are collinear with

\boldsymbol{c}

and

\boldsymbol{a}

respectively, then find

\boldsymbol{a} + \boldsymbol{b} + \boldsymbol{c}