Let \(ABC\) be a triangle such that \(\overrightarrow{ BC }=\overrightarrow{ a }, \overrightarrow{ CA }=\overrightarrow{ b }\), \(\overrightarrow{ AB }=\overrightarrow{ c },|\overrightarrow{ a }|=6 \sqrt{2}, \quad|\overrightarrow{ b }|=2 \sqrt{3}\) and \(\overrightarrow{ b } \cdot \overrightarrow{ c }=12\) Consider the statements. \(( S 1):|(\overrightarrow{ a } \times \overrightarrow{ b })+(\overrightarrow{ c } \times \overrightarrow{ b })|-|\overrightarrow{ c }|=6(2 \sqrt{2}-1)\) \(( S 2): \angle ABC =\cos ^{-1}\left(\sqrt{\frac{2}{3}}\right)\). Then

1. A both \(( S 1)\) and \(( S 2)\) are true 
2. B only \((S1)\) is true
3. C only \((S 2)\) is true
4. D both \(( S 1)\) and \(( S 2)\) are false