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MathsJEE Main 22 Jan 2026, Shift 2·Q21·Numerical·Moderate

Vectors · Angle between vectors

Let a vector a⃗=2i^−j^+λk^\vec a = \sqrt2\hat i - \hat j + \lambda\hat k, λ>0\lambda > 0, make an obtuse angle with the vector b⃗=−λ2i^+42j^+42k^\vec b = -\lambda^2\hat i + 4\sqrt2\hat j + 4\sqrt2\hat k and an angle θ\theta, π6<θ<π2\dfrac{\pi}{6} < \theta < \dfrac{\pi}{2}, with the positive zz-axis. If the set of all possible values of λ\lambda is (α,β)−{γ}(\alpha, \beta) - \{\gamma\}, then α+β+γ\alpha + \beta + \gamma is equal to .

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