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Vector Algebra question

2024 · 30 Jan · Shift 1 · Q34

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JEE Main
Mathematics
Vector Algebra
2024 · 30 Jan · Shift 1 · Q34

Vector Algebra question

2024 · 30 Jan · Shift 1 · Q34

JEE MainMathematicsVector AlgebraMCQ+4 / −1

Let

\overrightarrow{\mathrm{a}}=\mathrm{a}_1 \hat{i}+\mathrm{a}_2 \hat{j}+\mathrm{a}_3 \hat{k}

and

\overrightarrow{\mathrm{b}}=\mathrm{b}_1 \hat{i}+\mathrm{b}_2 \hat{j}+\mathrm{b}_3 \hat{k}

be two vectors such that

|\overrightarrow{\mathrm{a}}|=1, \vec{a} \cdot \vec{b}=2

and

|\vec{b}|=4

. If

\vec{c}=2(\vec{a} \times \vec{b})-3 \vec{b}

, then the angle between

\vec{b}

and

\vec{c}

is equal to:

A
$\cos ^{-1}\left(-\frac{1}{\sqrt{3}}\right)$
B
$\cos ^{-1}\left(\frac{2}{3}\right)$
C
$\cos ^{-1}\left(\frac{2}{\sqrt{3}}\right)$
D
$\cos ^{-1}\left(-\frac{\sqrt{3}}{2}\right)$

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