JEE Advanced 2024 Paper 1 Mathematics Q16

Mathematics

Problem

Let γ ∈ ℝ be such that the lines L₁ : (x + 11)/1 = (y + 21)/2 = (z + 29)/3 and L₂ : (x + 16)/3 = (y + 11)/2 = (z + 4)/γ intersect. Let R₁ be the point of intersection of L₁ and L₂. Let O = (0, 0, 0), and n^\hat{n} denote a unit normal vector to the plane containing both the lines L₁ and L₂. Match each entry in List-I to the correct entry in List-II. List-I: (P) γ equals, (Q) a possible choice for n^\hat{n} is, (R) OR₁⃗ equals, (S) a possible value of OR₁⃗ · n^\hat{n} is. List-II: (1) −î − ĵ + k^\hat{k}, (2) √(3/2), (3) 1, (4) (1/√6)î − (2/√6)ĵ + (1/√6)k^\hat{k}, (5) √(2/3). The correct option is

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