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 plane of \(\overrightarrow{a} \) and \(\overrightarrow{b} \), whose projection on \(\overrightarrow{c} \) is \(\frac{1}{\sqrt3}\), is given by,