If the shortest distance between the lines $\dfrac{x-\lambda}{2}=\dfrac{y-4}{3}=\dfrac{z-3}{4}$ and $\dfrac{x-2}{4}=\dfrac{y-4}{6}=\dfrac{z-7}{8}$ is $\dfrac{13}{\sqrt{29}}$, then a value of $\lambda$ is:
Step-by-Step Solution
Key Concept: Both lines have direction $\vec{b}=(2,3,4)$ (second is parallel: $(4,6,8)=2(2,3,4)$). So they are parallel. SD $=\frac{|\overrightarrow{a_1a_2}\times\vec{b}|}{|\vec{b}|}$. $a_2-a_1=(2-\lambda,0,4)$. $\vec{b}=(2,3,4)$.
$\lambda=1$ (taking positive value).
Correct Answer: 4