Let $$ABC$$ be a triangle such that $$\vec{BC} = \vec{a}$$, $$\vec{CA} = \vec{b}$$, $$\vec{AB} = \vec{c}$$, $$|\vec{a}| = 6\sqrt{2}$$, $$|\vec{b}| = 2\sqrt{3}$$ and $$\vec{b} \cdot \vec{c} = 12$$. Consider the statements:
$$S_1: |\vec{a} \times (\vec{b} + \vec{c})| \times |\vec{b} - \vec{c}| = 6(2\sqrt{2} - 1)$$
$$S_2: \angle ABC = \cos^{-1}\sqrt{\dfrac{2}{3}}$$
Then

A

both $$S_1$$ and $$S_2$$ are true

B

only $$S_1$$ is true

C

only $$S_2$$ is true

D

both $$S_1$$ and $$S_2$$ are false