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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
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.
The correct option is
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) | \(\sqrt{\frac{2}{3}}\) | ||
Updated On: Jun 10, 2024
- (P) → (3) (Q) → (4) (R) → (1) (S) → (2)
- (P) → (5) (Q) → (4) (R) → (1) (S) → (2)
- (P) → (3) (Q) → (4) (R) → (1) (S) → (5)
- (P) → (3) (Q) → (1) (R) → (4) (S) → (5)
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The Correct Option is C
Solution and Explanation
The correct option is (C):(P) → (3) (Q) → (4) (R) → (1) (S) → (5).
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