If \(\vec a = \hat i - \hat j + \hat k,\;\vec b = 2\hat i + 3\hat j + 2\hat k\) and \(\vec c = \hat i + m\hat j + n\hat k\) are three coplanar vectors and \(\left| {\vec c} \right| = \sqrt 6\), then which one of the following is correct?

• A. m = 2 and n = ± 1
• B. m = ± 2 and n = -1
• C. m = 2 and n = -1
• D. m = ± 2 and n = 1