Let $\vec{a} = \hat{i} + \hat{j} + \hat{k}$, $\vec{b} = \hat{i} - \hat{j} + \hat{k}$ and $\vec{c} = \hat{i} - \hat{j} - \hat{k}$ be three vectors. A vector $\vec{v}$ in the plane of $\vec{a}$ and $\vec{b}$, whose projection on $\vec{c}$ is $\frac{1}{\sqrt{3}}$, is\\
(1) $\hat{i} - 3\hat{j} + 3\hat{k}$\\
(2) $-3\hat{i} - 3\hat{j} - \hat{k}$\\
(3) $3\hat{i} - \hat{j} + 3\hat{k}$\\
(4) $\hat{i} + 3\hat{j} - 3\hat{k}$