If $\vec a,\vec b,\vec c$ are three non-zero vectors, no two of which are collinear and the vector $\vec a+\vec b$ is collinear with $\vec c$, $\vec b+\vec c$ is collinear with $\vec a$, then $\vec a+\vec b+\vec c=$

none of these

It is given that

$\vec a+\vec b$ is collinear with $\vec c$ and $\vec b+\vec c$ is collinear with $\vec a$.

$∴\vec a+\vec b=λ\vec c$ and $\vec b+\vec c =μ \vec a$

$⇒\vec a+\vec b=λ(μ\vec a-\vec b)$  [On eliminating $\vec c$]

$⇒(λμ-1)\vec a-(λ+1)\vec b=\vec 0$

$⇒λμ-1=0$ and $λ+1=0$  [∵$\vec a,\vec b$ bare non-collinear]

$⇒λ=-1$ and $μ=-1$

Substituting $λ=-1$ in $\vec a+\vec b=λ\vec c$, we get $\vec a+\vec b+\vec c=\vec 0$