Mathematics

Problem

Let

\vec{a}

\vec{b}

and

\vec{c}

be three non-zero vectors such that no two of these are collinear. If the vector

\vec{a}+2\vec{b}

is collinear with

\vec{c}

and

\vec{b}+3\vec{c}

is collinear with

\vec{a}

(

\lambda

being some non-zero scalar), then

\vec{a}+2\vec{b}+6\vec{c}

equals A.

\lambda \vec{a}

\lambda \vec{b}

\lambda \vec{c}

\vec{0}