Question

The lines $\frac{x+2}{4\lambda +1}=\frac{y-1}{4}=\frac{z}{-18}$ and$\frac{x}{-3}=\frac{y+1}{5\mu -3}=\frac{z-1}{6}$ are parallel to each other, then the value of the pair $(\lambda ,\mu )$ is

• A. $(-2,\frac{1}{3})$
• B. $(2,-\frac{1}{3})$
• C. $(2,\frac{1}{3})$
• D. Cannot be found

Answer 1

Answer: (C)

$(2,\frac{1}{3})$

Lines $\frac{x+2}{4\lambda +1}=\frac{y-1}{4}=\frac{z}{-18}$ and $\frac{x}{-3}=\frac{y+1}{5\mu -3}=\frac{z-1}{6}$ are parallel to each other. Ratio of direction cosines will be same.
$\frac{4\lambda +1}{-3}=\frac{-18}{6}$ and $\frac{4}{5\mu -3}=\frac{-18}{6}$
$4\lambda +1=9$ and $4=-15\mu +9$
$4\lambda =8$ and $15\mu =5$
$\lambda =2$ and $\mu =\frac{1}{3}$
$\therefore (\lambda ,\mu )=(2,\frac{1}{3})$