Let the shortest distance between the lines and be . If lies on , then which of the following is NOT possible ?

Explanation: The Solution Step 1: Convert lines to standard vector form To find the shortest distance, we need a point on each line and their direction vectors. For Line : * Point Direction vector For Line : (Rewriting ) Point Direction vector Step 2: Find the Shortest Distance (S.D.) The formula for S.D. is: Calculate : Calculate : Calculate Magnitude Plug into the S.D. formula: Since , we get . Step 3: Analyze point on Since is on , its coordinates must satisfy: From this, we extract the relationship between and : Equating the two expressions for : Conclusion We found that for any point on line , the relation must be true. Looking at the options: Option (4) says . This contradicts our finding that . Therefore, Option (4) is NOT possible .

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JEE 2023 — Mathematics PYQ

JEE | Mathematics | 2023

Let the shortest distance between the lines $L : \frac{x - 5}{- 2} = \frac{y - λ}{0} = \frac{z + λ}{1}, λ \geq 0$ and $L_{1} : x + 1 = y - 1 = 4 - z$ be $2\sqrt{6}$ . If $(\alpha, \beta, \gamma)$ lies on $L$ , then which of the following is NOT possible?

JEE 2023 — Mathematics PYQ

Choose the correct answer:

Explanation

The Solution

Step 1: Convert lines to standard vector form

Step 2: Find the Shortest Distance (S.D.)

Step 3: Analyze point $(\alpha, \beta, \gamma)$ on $L$

Conclusion