Let $$\overrightarrow{a} = \hat{i} + \hat{j} + \hat{k}, \overrightarrow{b} = \hat{i} - \hat{j} + \hat{k}$$ and $$\overrightarrow{c} = \hat{i} - \hat{j} - \hat{k}$$ be three vectors. A vector $$\overrightarrow{v}$$ in the place of $$\overrightarrow{a}$$ and $$\overrightarrow{b}$$, whose projection on $$\overrightarrow{c}$$ is $$\frac{1}{\sqrt{3}}$$, is given by

A

$$\hat{i} - 3 \hat{j} + 3 \hat{k}$$

B

$$-3 \hat{i} - 3 \hat{j} - \hat{k}$$

C

$$3 \hat{i} - \hat{j} + 3 \hat{k}$$

D

$$\hat{i} + 3 \hat{j} - 3 \hat{k}$$