JEE Advanced 2026 Mathematics question

MathematicsVector AlgebraJEE Advanced 2026

For real numbers α, β, γ, δ and µ, consider the matrix

M = .

Suppose that , where is the transpose of the matrix M, and I is the 3 × 3 identity matrix. Let

Missing argument for \vec\vec u = αMissing argument for \hat\hat i + Missing argument for \hat\hat j + γMissing argument for \hat\hat k, Missing argument for \vec\vec v = Missing argument for \hat\hat i + βMissing argument for \hat\hat j + δMissing argument for \hat\hat k and Missing argument for \vec\vec w = -Missing argument for \hat\hat i + Missing argument for \hat\hat j + μMissing argument for \hat\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 is (Q) If for some real numbers x, y and z, then the value of x is (R) The value of is (S) The value of is List-II (1) 0 (2) 1 (3) (4) (5)

Answer: (A)

Solution

M is orthogonal, so its rows and its columns are orthonormal. Row 1: ; column 1: ; row 2: ; column 2: . (P) $γ^2 +

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Question ID VK-104719