Let the shortest distance between the lines L: (x-5/-2)=(y-λ/0)=(z+λ/1), λ ≥ 0 and L1: x+1=y-1=4-z be 2 √6. If (α, β, γ) lies on L, then which of the following is NOT possible?

Question

Let the shortest distance between the lines L: (x-5/-2)=(y-λ/0)=(z+λ/1), λ ≥ 0 and L1: x+1=y-1=4-z be 2 √6. If (α, β, &gamma;) lies on L, then which of the following is NOT possible? (A) α+2 y=24 (B) 2 α+&gamma;=7 (C) α-2 &gamma;=19 (D) 2 α-&gamma;=9

Tardigrade Admin · Accepted Answer

Q. 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 $26$ . If $(α, β, γ)$ lies on $L$ , then which of the following is NOT possible?

$α + 2 y = 24$

$2 α + γ = 7$

$α - 2 γ = 19$

$2 α - γ = 9$

Q. Let the shortest distance between the lines L:−2x−5​=0y−λ​=1z+λ​,λ≥0 and L1​:x+1=y−1=4−z be 26​. If (α,β,γ) lies on L, then which of the following is NOT possible?

α+2y=24

2α+γ=7

α−2γ=19

2α−γ=9

b1​​×b2​​=∣∣​i^−21​j^​01​k^1−1​∣∣​=−i^−j^​−2k^ a2​​−a1​​=6i^+(λ−1)j^​+(−λ−4)k^ 26​=∣∣​1+1+4​−6−λ+1+2λ+8​∣∣​ ∣λ+3∣=12⇒λ=9,−15 α=−2k+5,γ=k−λ where k∈R ⇒α+2γ=5−2λ=−13,35

Q. 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 $26$ . If $(α, β, γ)$ lies on $L$ , then which of the following is NOT possible?

$α + 2 y = 24$

$2 α + γ = 7$

$α - 2 γ = 19$

$2 α - γ = 9$