Let $ABC$ be a triangle such that $\overrightarrow { BC } = \vec { a }$, $\overrightarrow { CA } = \vec { b }$, $\overrightarrow { AB } = \vec { c }$, $|\vec{a}| = 6\sqrt{2}$, $|\vec{b}| = 2\sqrt{3}$ and $\vec{b} \cdot \vec{c} = 12$. Consider the statements: S1: $|\vec{a} \times \vec{b} + \vec{c} \times \vec{b}| - |\vec{c}| = 6(2\sqrt{2} - 1)$ S2: $\angle ABC = \cos^{-1}\sqrt{\frac{2}{3}}$. Then (1) both $S1$ and $S2$ are true (2) only $S1$ is true (3) only $S2$ is true (4) both $S1$ and $S2$ are false
Let $ABC$ be a triangle such that $\overrightarrow { BC } = \vec { a }$, $\overrightarrow { CA } = \vec { b }$, $\overrightarrow { AB } = \vec { c }$, $|\vec{a}| = 6\sqrt{2}$, $|\vec{b}| = 2\sqrt{3}$ and $\vec{b} \cdot \vec{c} = 12$. Consider the statements:\\
S1: $|\vec{a} \times \vec{b} + \vec{c} \times \vec{b}| - |\vec{c}| = 6(2\sqrt{2} - 1)$\\
S2: $\angle ABC = \cos^{-1}\sqrt{\frac{2}{3}}$. Then\\
(1) both $S1$ and $S2$ are true\\
(2) only $S1$ is true\\
(3) only $S2$ is true\\
(4) both $S1$ and $S2$ are false