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Vector Algebra question

2022 · 25 Jul · Shift 1 · Q34

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JEE Main
Mathematics
Vector Algebra
2022 · 25 Jul · Shift 1 · Q34

Vector Algebra question

2022 · 25 Jul · Shift 1 · Q34

JEE MainMathematicsVector AlgebraMCQ+4 / −1

Let

\mathrm{ABC}

be a triangle such that

\overrightarrow{\mathrm{BC}}=\overrightarrow{\mathrm{a}}, \overrightarrow{\mathrm{CA}}=\overrightarrow{\mathrm{b}}, \overrightarrow{\mathrm{AB}}=\overrightarrow{\mathrm{c}},|\overrightarrow{\mathrm{a}}|=6 \sqrt{2},|\overrightarrow{\mathrm{b}}|=2 \sqrt{3}

and

\vec{b} \cdot \vec{c}=12

. Consider the statements :

(\mathrm{S} 1):|(\overrightarrow{\mathrm{a}} \times \overrightarrow{\mathrm{b}})+(\overrightarrow{\mathrm{c}} \times \overrightarrow{\mathrm{b}})|-|\vec{c}|=6(2 \sqrt{2}-1)(\mathrm{S} 2): \angle \mathrm{ACB}=\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

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