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

• A. 3î - ĵ + 3k̂
• B. î - 3ĵ + 3k̂
• C. 5î - 2ĵ + 5k̂
• D. 2î - ĵ + 3k̂