The position vector of the point on the line \(\vec r = \hat i + \lambda (\hat i + \hat j + \hat k)\) whose distance from \(\vec r - (\hat i + \hat j) (\hat i - \hat j - \hat k) = 1\) is \(\frac 1{\sqrt3}\) units is
(a) \(-\hat i - \hat j - 2\hat k\)
(b) \(\hat j\)
(c) \(2\hat i +\hat j+ \hat k\)
(d) \(3\hat i +2\hat j+ 2\hat k\)