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Vector Algebra question

2022 · 28 Jul · Shift 2 · Q33

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JEE Main
Mathematics
Vector Algebra
2022 · 28 Jul · Shift 2 · Q33

Vector Algebra question

2022 · 28 Jul · Shift 2 · Q33

JEE MainMathematicsVector AlgebraMCQ+4 / −1

Let S be the set of all a

\in R

for which the angle between the vectors

\vec{u}=a\left(\log _{e} b\right) \hat{i}-6 \hat{j}+3 \hat{k}

and

\vec{v}=\left(\log _{e} b\right) \hat{i}+2 \hat{j}+2 a\left(\log _{e} b\right) \hat{k}

,

(b\gt 1)

is acute. Then S is equal to :

A
$\left(-\infty,-\frac{4}{3}\right)$
B
$\Phi$
C
$\left(-\frac{4}{3}, 0\right)$
D
$\left(\frac{12}{7}, \infty\right)$

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