Let a vector \overrightarrow{ a }=\sqrt{2} \hat{i}-\hat{j}+\lambda \hat{k}, \lambda>0, make an obtuse angle with the vector \overrightarrow{ b }=-\lambda^2 \hat{i}+4 \sqrt{2} \hat{j}+4 \sqrt{2} \hat{k} and an angle \theta, \frac{\pi}{6}< \theta< \frac{\pi}{2}, with the positive z-axis. If the set of all possible values of \lambda is (\alpha, \beta)-\{\gamma\}, then \alpha+\beta+\gamma is equal to \_\_\_\_ . [22 Jan 2026 Shift 2]

JEE Main 22 Jan 2026 Shift 2 Paper Solved Paper

Section: Mathematics

Question : 22 of 75

Marks: +1, -0

Let a vector

→

=√2

∧

−

∧

+λ

∧

,λ>0, make an obtuse angle with the vector

→

=−λ2

∧

+4√2

∧

+4√2

∧

and an angle θ,‌

<θ<‌

, with the positive z-axis. If the set of all possible values of λ is (α,β)−{γ}, then α+β+γ is equal to ____ .

[22 Jan 2026 Shift 2]

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