JEE Advanced 2025 Paper 1 Mathematics Q16

Mathematics

Problem

Let w⃗\vec{w} = î + ĵ − 2k^\hat{k}, and u⃗\vec{u} and v⃗\vec{v} be two vectors, such that u⃗\vec{u} × v⃗\vec{v} = w⃗\vec{w} and v⃗\vec{v} × w⃗\vec{w} = u⃗\vec{u}. Let α, β, γ, and t be real numbers such that u⃗\vec{u} = αî + βĵ + γk^\hat{k}, −tα + β + γ = 0, α − tβ + γ = 0, and α + β − tγ = 0. Match each entry in List-I to the correct entry in List-II and choose the correct option. List-I: (P) |v⃗\vec{v}|²; (Q) if α = √3, then γ²; (R) if α = √3, then (β + γ)²; (S) if α = √2, then t + 3. List-II: (1) 0; (2) 1; (3) 2; (4) 3; (5) 5.

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