Question

The direction ratios of two parallel lines are $4,-3,-1$ and $\lambda +\mu ,1+\mu ,2$. The value of the pair $(\lambda ,\mu )$ is

• A. $(13,5)$
• B. $(-13,5)$
• C. $(5,13)$
• D. $(5,-13)$

Answer 1

Answer: (B)

$(-13,5)$

Since the direction ratios of two parallel lines are $4,-3,-1$ and $\lambda +\mu ,1+\mu ,2$
Therefore, $\frac{4}{\lambda +\mu }=\frac{-3}{1+\mu }=\frac{-1}{2}$
$\Rightarrow \lambda +\mu =-8$
and $1+\mu =6$
by solving simultaneously $(\lambda ,\mu )=(-13,5)$