Question

Let y ∈ R be such that the lines \(L_1:\frac{x+11}{1}=\frac{y+21}{2}=\frac{z+29}{3}\) and \(L_2:\frac{x+16}{3}=\frac{y+11}{2}=\frac{z+4}{\gamma}\) intersect. Let R₁ be the point of intersection of L₁ and L₂. Let O = (0, 0 ,0), and \(\hat{n}\) denote a unit normal vector to the plane containing both the lines L₁ and L₂.
Match each entry in List-I to the correct entry in List-II.

List - I		List - II
(P)	γ equals	(1)	\(-\hat{i}-\hat{j}+\hat{k}\)
(Q)	A possible choice for \(\hat{n}\) is	(2)	\(\sqrt{\frac{3}{2}}\)
(R)	\(\overrightarrow{OR_1}\) equals	(3)	1
(S)	A possible value of \(\overrightarrow{OR_1}.\hat{n}\) is	(4)	\(\frac{1}{\sqrt6}\hat{i}-\frac{2}{\sqrt6}\hat{j}+\frac{1}{\sqrt6}\hat{k}\)
		(5)	\(\sqrt{\frac{2}{3}}\)

The correct option is

• A. (P) → (3) (Q) → (4) (R) → (1) (S) → (2)
• B. (P) → (5) (Q) → (4) (R) → (1) (S) → (2)
• C. (P) → (3) (Q) → (4) (R) → (1) (S) → (5)
• D. (P) → (3) (Q) → (1) (R) → (4) (S) → (5)

Answer 1

The Correct Option is C

The correct option is (C):(P) → (3) (Q) → (4) (R) → (1) (S) → (5).