Let ₁ and ₂ be the lines {r}₁=λ({i}+{j}+{k}) and {r}₂=({j}-{k})+({i}+{k}), respectively, Let X be the set of all the planes H that contain the line . For a plane H, let d(H) denote the smallest possible distance between the points of ₂ and H. Let H₀ be a plane in X for which d(H₀) is the maximum value of d(H) as H varies over all planes in x. Match each entry in List-I to the correct entries in List-II. List-I List-II (P) The value of d(H₀) is (1) {3} (Q) The distance of the point (0,1,2) from H₀ is (2) \;{1}{{3}} (R) The distance of origin from H₀ is (3) 0 (S) The distance of origin from the point of intersection of planes y=z, x=1 and H₀ is (4) \;{2} (5) {1}{{2}} The correct option is [JEE Adv 2023 P1]

Question

Examsnet · Accepted Answer

Correct Answer is : (P)→(5)(Q)→(4)(R)→(P)arrow(5)(Q)arrow(4)(R)arrow(P)→(5)(Q)→(4)(R)→ (3) (S) →arrow→ (1)

List-I	List-II
(P) The value of $d(H_0)$ is	(1) $\sqrt{3}$
(Q) The distance of the point $(0,1,2)$ from $H_0$ is	(2) $\;\frac{1}{\sqrt{3}}$
(R) The distance of origin from $H_0$ is	(3) 0
(S) The distance of origin from the point of intersection of planes $y=z, x=1$ and $H_0$ is	(4) $\;\sqrt{2}$
	(5) $\frac{1}{\sqrt{2}}$

JEE Advanced 2023 Paper 1 Solutions