JEE Advanced 2026 Paper 1 Mathematics Q15

Mathematics

Problem

For real numbers α, β, γ, δ and μ, consider the matrix M = [[α, 1/√2, −1/√2], [1/√3, β, 1/√3], [γ, δ, μ]]. Suppose that MMᵀ = I, where Mᵀ is the transpose of the matrix M, and I is the 3 × 3 identity matrix. Let u⃗\vec{u} = αî + (1/√3)ĵ + γk^\hat{k}, v⃗\vec{v} = (1/√2)î + βĵ + δk^\hat{k} and w⃗\vec{w} = −(1/√2)î + (1/√3)ĵ + μk^\hat{k}. Match each entry in List-I to the correct entry in List-II and choose the correct option. List-I: (P) The value of γ² + δ² is; (Q) If xu⃗\vec{u} + yv⃗\vec{v} + zw⃗\vec{w} = ĵ for some real numbers x, y and z, then the value of x is; (R) The value of |u⃗\vec{u} · (v⃗\vec{v} × w⃗\vec{w})| is; (S) The value of |u⃗\vec{u} × (v⃗\vec{v} × w⃗\vec{w})| is. List-II: (1) 0; (2) 1; (3) 1/√2; (4) 1/√3; (5) 5/6.

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