Let $l_{1}$ and $l_{2}$ be the lines $\vec{r_{1}} = λ (\hat{i} + \hat{j} + \hat{k})$ and $\vec{r_{2}} = (\hat{j} - \hat{k}) + μ (\hat{i} + \hat{k}),$ respectively. Let X be the set of all the planes H that contain the line $l_{1} .$ For a plane H, let d(H) denote the smallest possible distance between the points of $l_{2}$ and H. Let $H_{0}$ be plane in X for which $d (H_{0})$ is the maximum value of d(H) as 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 $d (H_{0})$ is 1) 0
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) $\sqrt{3}$
S)
The distance of origin from the point of intersection of planes
y =z, x= 1 and $H_{0}$ is
4) $\sqrt{2}$
5) $\frac{1}{\sqrt{2}}$
The correct option is :

see full answer

21% of IItians & 23% of AIIMS delhi doctors are from Sri Chaitanya institute !!

An Intiative by Sri Chaitanya

$P \to 5; Q \to 4; R \to 1; S \to 3$

$P \to 2; Q \to 3; R \to 1; S \to 2$

$P \to 2; Q \to 4; R \to 5; S \to 3$

$P \to 5; Q \to 3; R \to 4; S \to 2$

answer is B.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Detailed Solution

Watch 3-min video & get full concept clarity

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