Question

Let the shortest distance between the lines $L: \frac{x-5}{-2}=\frac{y-\lambda}{0}=\frac{z+\lambda}{1}, \lambda \geq 0$ 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?

• A. $\alpha+2 y=24$
• B. $2 \alpha+\gamma=7$
• C. $\alpha-2 \gamma=19$
• D. $2 \alpha-\gamma=9$

Answer 1

Answer: (A)

$\alpha+2 y=24$

Answer 2

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