The least positive integral value of , for which the angle between the vectors and is acute, is

5 Explanation: Since, the angle is acute Least value of

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JEE 2024 — Mathematics PYQ

JEE | Mathematics | 2024

The least positive integral value of $α$ , for which the angle between the vectors $\overset{a}{^} \hat{i} - 2 \hat{j} + 2 \hat{k}$ and $α \hat{i} + 2 \overset{a}{^} \hat{j} - 2 \hat{k}$ is acute, is

Choose the correct answer:

A.
1
B.
2
C.
5
(Correct Answer)
D.
4

Correct Answer:

Explanation

Since, the angle is acute
$∴ cos θ ⩾ 0$
$\Rightarrow (α^{2} - 4 α - 41 ⩾ 0)$
$\Rightarrow (α - 2)^{2} ⩾ 8$
$\Rightarrow ∣ α - 2∣ ⩾ 22$
$∴ α \in (- \infty, - 22 + 2) \cup [2 + 22; \infty)$
$∴$ Least value of $α = 5$

Explanation

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