For three vectors \(\vec A = 2\hat j - 3\hat k,\vec B = - 2\hat i + \hat k\ and\;\hat C = 3\hat i - \hat j,\) where î, ĵ and k̂ are unit vectors along the axes of a right-handed rectangular/Cartesian coordinate system, the value of \(\left( {\overrightarrow {A.} \left( {\vec B \times \vec C} \right) + 6} \right)\) is _______.
Enter numerical value using the virtual keypad. Round off where necessary.