The direction ratios of two parallel lines are 4,-3,-1 and λ + μ,1+μ,2 . The value of the pair (λ,μ) is

(1,7)

(-1,-7)

(7,1)

No fixed value

Question

The direction ratios of two parallel lines are 4,-3,-1 and
λ + μ,1+μ,2 The value of the pair (λ,μ)
is

(1,7)
(-1,-7)
(7,1)
No fixed value

Ajanta Trivedi · Accepted Answer

if your query is :

the direction ratios of two parallel lines are 4, 3, -1 and $λ + μ, 1 + μ, 2$ . the value of the pair $(λ, μ)$ is ??

if $a_{1}, b_{1}, c_{1} a n d a_{2}, b_{2}, c_{2}$ are the direction ratios of two parallel lines .

therefore

$\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} = \frac{c_{1}}{c_{2}}$ .............(1)

hence

$\frac{4}{λ + μ} = \frac{3}{1 + μ} = \frac{- 1}{2} \Rightarrow λ + μ = - 8 ............ (2) 1 + μ = - 6....... (3)$

therefore

$μ = - 6 - 1 = - 7 a n d λ = - 8 - μ = - 8 + 7 = - 1$

hope this helps you.

cheers!!