Question

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}\left(\sqrt{\frac{2}{3}}\right) Then

• A. both (S1) and (S2) are true
• B. only (S1) is true
• C. only (S2) is true
• D. both (S1) and (S2) are false

Answer 1

Answer: (C)

only (S2) is true

Answer 2

The correct option is (C): only (S2) is true