Let the vectors $\vec a=(1+t)\hat i+(1-t)\hat j+\hat k$, $\vec b=(1-t)\hat i+(1+t)\hat j+2\hat k$ and $\vec c=t\hat i-t\hat j+\hat k$, $t\in\mathbb R$ be such that for $\alpha,\beta,\gamma\in\mathbb R$, $\alpha\vec a+\beta\vec b+\gamma\vec c=\vec 0\Rightarrow \alpha=\beta=\gamma=0$. Then, the set of all values of $t$ is: