If the lines given by $\frac{x-1}{2 \lambda}=\frac{y-1}{-5}=\frac{z-1}{2}$ and…
If the lines given by $\frac{x-1}{2 \lambda}=\frac{y-1}{-5}=\frac{z-1}{2}$ and $\frac{x+2}{\lambda}=\frac{y+3}{\lambda}=\frac{z+5}{1}$ are parallel, then the value $\lambda$ is
$\frac{-2}{5}$
$\frac{2}{5}$
$\frac{5}{2}$
$\frac{-5}{2}$
Solution
Line $\frac{x-1}{2 \lambda}=\frac{y-1}{-5}=\frac{z-1}{2}$ has direction ratios $2 \lambda,-5,2$
Line $\frac{x+2}{\lambda}=\frac{y+3}{\lambda}, \frac{z+5}{1}$ has direction ratios $\lambda, \lambda, 1$
Since lines are parallel, $\frac{2 \lambda}{\lambda}=\frac{-5}{\lambda}=\frac{2}{1} \Rightarrow \lambda=\frac{-5}{2}$