If the lines $\frac{x-4}{1}=\frac{y-2}{1}=\frac{z-λ}{3}$ and $\frac{x}{1}=\frac{y+2}{2}=\frac{z}{4}$ intersect each other, then λ lies in the interval
Answer & explanation
Correct answer: option 4
Given lines will intersect, if
$\begin{vmatrix}4-0 & 2-(-2) & λ-0\\1 & 1 & 3\\1 & 2 & 4\end{vmatrix}=0$
$⇒ 4(4-6) -4(4-3) + λ(2-1)= 0 $
$⇒ λ = 12 ⇒ λ \,\, ∈ (11, 13)$