A vector \(\vec{c}\), perpendicular to the vectors \(\overrightarrow a = \hat i - 2\hat j + 3\hat k\) and \(\overrightarrow b = 2\hat i + 3\hat j - \hat k\), and satisfying \(\overrightarrow c .\left( {2\hat i + \hat j - \hat k} \right) = - 7\), is?
1
\(\frac{7}{2}\left( {\hat i - \hat j + \hat k} \right)\)
2
\(\frac{7}{2}\left( { - \hat i + \hat j + \hat k} \right)\)
3
7(î - ĵ + k̂)
4
7(-î + ĵ + k̂)