3D Geometry PYQ — JEE Advanced 2023 · Shift 1 · Q33 with Solution

Let

\ell_1

and

\ell_2

be the lines

\vec{r}_1=\lambda(\hat{i}+\hat{j}+\hat{k})

and

\vec{r}_2=(\hat{j}-\hat{k})+\mu(\hat{i}+\hat{k})

, respectively. Let

X

be the set of all the planes

H

that contain the line

\ell_1

. For a plane

H

, let

d(H)

denote the smallest possible distance between the points of

\ell_2

and

H

. Let

H_0

be a plane in

X

for which

d\left(H_0\right)

is the maximum value of

d(H)

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 $d\left(H_0\right)$ 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) $\frac{1}{\sqrt{2}}$

The correct option is:

A
$(P) \rightarrow(2) \quad(Q) \rightarrow(4) \quad(R) \rightarrow(5) \quad(S) \rightarrow(1)$
B
$(P) \rightarrow(5) \quad(Q) \rightarrow(4) \quad(R) \rightarrow(3) \quad(S) \rightarrow(1)$
C
$(P) \rightarrow(2) \quad(Q) \rightarrow(1) \quad(R) \rightarrow(3) \quad(S) \rightarrow(2)$
D
$(P) \rightarrow(5) \quad(Q) \rightarrow(1) \quad(R) \rightarrow(4) \quad(S) \rightarrow(2)$

3D Geometry question