JEE Main 2022 · 28 Jul · Shift 2 · Mathematics Q77

← JEE Main 2022 · 28 Jul · Shift 2

MathematicsSingle correct+4 / -1Question 77 of 90

Let S be the set of all $a\in\mathbf R$ for which the angle between the vectors $\vec u=a(\log_eb)\hat i-6\hat j+3\hat k$ and $\vec v=(\log_eb)\hat i+2\hat j+2a(\log_eb)\hat k$ , $(b>1)$ is acute. Then S is equal to :

\left(-\infty,-\dfrac43\right)

\Phi

\left(-\dfrac43,0\right)

\left(\dfrac{12}7,\infty\right)

Answer and worked solution

Official answer: B

Acute needs $aL^2+6aL-12>0$ for every $L=\ln b>0$ . As $L\to0^+$ this tends to $-12$ , so no a works.

$S=\Phi$ . (B)

Topics:Dot product Inequalities and modulus

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JEE Main 2022 · 28 Jul · Shift 2, Mathematics question 77