Let \({\rm{\vec a}} = \hat i + 2{\rm{\hat j}} + 4{\rm{\hat k}},\;{\rm{\vec b}} = {\rm{\hat i}} + \lambda {\rm{\hat j}} + 4{\rm{\hat k}},{\rm{\;and\;\vec c}} = 2{\rm{\hat i}} + 4{\rm{\hat j}} + \left( {{\lambda ^2} - 1} \right){\rm{\hat k}}\) be coplanar vectors. Then the non-zero vector \({\rm{\vec a}} \times {\rm{\vec c}}\) is:

• A. \(- 10\hat i - 5{\rm{\hat j}}\)
• B. \(- 14\hat i - 5{\rm{\hat j}}\)
• C. \(- 14\hat i + 5{\rm{\hat j}}\)
• D. \(- 10\hat i + 5{\rm{\hat j}}\)