Question

Let $\gamma \in \mathbb{R}$ be such that the lines $\mathrm{L}_{1}: \frac{\mathrm{x}+11}{1}=\frac{\mathrm{y}+21}{2}=\frac{\mathrm{z}+29}{3}$ and $\mathrm{L}_{2}: \frac{\mathrm{x}+16}{3}=\frac{\mathrm{y}+11}{2}=\frac{\mathrm{z}+4}{\gamma}$ intersect. Let $\mathrm{R}_{1}$ be the point of intersection of $\mathrm{L}_{1}$ and $\mathrm{L}_{2}$. Let $\mathrm{O}=(0,0,0)$, and $\hat{\mathrm{n}}$ denote a unit normal vector to the plane containing both the lines $\mathrm{L}_{1}$ and $\mathrm{L}_{2}$.

Match each entry in List-I to the correct entry in List-II.

| List-I | | List-II | |
| --- | --- | --- | --- |
| (P) | $\gamma$ equals | (1) | $-\hat{\mathrm{i}}-\hat{\mathrm{j}}+\hat{\mathrm{k}}$ |
| (Q) | A possible choice for $\hat{\mathrm{n}}$ is | (2) | $\sqrt{\frac{3}{2}}$ |
| (R) | $\overline{\mathrm{OR}}_{1}$ equals | (3) | 1 |
| (S) | A possible value of $\mathrm{OR}_{1}$. $\hat{\mathrm{n}}$ is | (4) | $\frac{1}{\sqrt{6}} \hat{\mathrm{i}}-\frac{2}{\sqrt{6}} \hat{\mathrm{j}}+\frac{1}{\sqrt{6}} \hat{\mathrm{k}}$ |
| | | (5) | $\sqrt{\frac{2}{3}}$ |

The correct option is

Accepted Answer

(C) $(\mathrm{P}) \rightarrow(3)(\mathrm{Q}) \rightarrow(4) \quad(\mathrm{R}) \rightarrow(1)(\mathrm{S}) \rightarrow(5)$

Answer

(A) $(\mathrm{P}) \rightarrow(3)(\mathrm{Q}) \rightarrow(4) \quad(\mathrm{R}) \rightarrow(1)(\mathrm{S}) \rightarrow(2)$

Answer

(B) $(\mathrm{P}) \rightarrow(5)(\mathrm{Q}) \rightarrow(4) \quad(\mathrm{R}) \rightarrow(1)(\mathrm{S}) \rightarrow(2)$

Answer

(D) $(\mathrm{P}) \rightarrow(3)(\mathrm{Q}) \rightarrow(1) \quad(\mathrm{R}) \rightarrow(4)(\mathrm{S}) \rightarrow(5)$

JEE Advanced · 2024 · 26 May 2024 · Paper 1 · Three Dimensional Geometry

Solution

More JEE Advanced questions on Three Dimensional Geometry

List-I		List-II
(P)	$γ$ equals	(1)	$- \hat{i} - \hat{j} + \hat{k}$
(Q)	A possible choice for $\overset{n}{^}$ is	(2)	$\frac{3}{2}$
(R)	$\overline{OR}_{1}$ equals	(3)	1
(S)	A possible value of $OR_{1}$ . $\overset{n}{^}$ is	(4)	$\frac{1}{6} \hat{i} - \frac{2}{6} \hat{j} + \frac{1}{6} \hat{k}$
		(5)	$\frac{2}{3}$