∣a∣a.k^=cosθ⇒3+λ2λ=cosθ
⇒0<3+λ2λ<23
⇒λ>0&4λ2<9+3λ2⇒λ2<9
⇒λ∈(0,3)….(1)
⇒a⋅ b<0⇒−2λ2−42+42λ<0
⇒λ2−4λ+4>0⇒(λ−2)2>0
⇒λ=2
from (1)&(2)
λ∈(0,3)−{2}
∴α=0,β=3,γ=2
⇒α+β+γ=5
JEE Main 2026 — Mathematics Vectors & 3D Geometry
Let a vector a=2i^−j^+λk^,λ>0, make an obtuse angle with the vector b=−λ2i^+42j^+42k^ and an angle θ,6π<θ<2π, 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 ____。
Held on 22 Jan 2026 · Verified 6 Jul 2026.
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