JEE Advanced 2023 Paper 1 Mathematics Q16

Mathematics

Problem

Let ℓ₁ and ℓ₂ be r⃗1\vec{r}_{1}=λ(î+ĵ+k^\hat{k}) and r⃗2\vec{r}_{2}=(ĵ−k^\hat{k})+μ(î+k^\hat{k}), respectively. Let X be all planes H containing ℓ₁. For H, let d(H) be the smallest distance between points of ℓ₂ and H, and let H₀ maximize d(H). List-I: (P) d(H₀); (Q) distance of (0,1,2) from H₀; (R) distance of the origin from H₀; (S) distance of the origin from the intersection of y=z, x=1 and H₀. List-II: (1) √3, (2) 1/√3, (3) 0, (4) √2, (5) 1/√2. The correct option is:

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