Let $$\overrightarrow{a}= 2\widehat{i}-\widehat{j}-\widehat{k}, \overrightarrow{b}=\widehat{i}+ 3\widehat{j}-\widehat{k}$$ and $$\overrightarrow{c} = 2\widehat{i}+\widehat{j}+3\widehat{k}.$$ Let $$\overrightarrow{\nu}$$ be the vector in the plane of the vectors $$\overrightarrow{a}$$ and $$\overrightarrow{b}$$, such that the length of its projection on the vector $$\overrightarrow{C}$$ is $$\frac{1}{\sqrt{14}}$$. Then $$\mid \overrightarrow{\nu} \mid$$ is euqal to