If the lines (x-3)/2=(y-5)/2=(z-4)/(λ) and (x-2)/(λ)=(y-6)/4=(z-5)/2 intersect at a point α,β,γ, then the greatest value of λ is equal to

Correct answer: (A) 0. Two given lines intersect ⇒ they must be coplanar So, 3-2 5-6 4-5 2 2 λ λ 4 2 =0 ⇒14-4λ+14-λ^2-18-2λ=0 ⇒4-4λ+4-λ^2-8+2λ=0 ⇒λ^2+2λ=0⇒λ=0,-2

Q34 / 105 · NTA Abhyas (JEE Main) 2020 · Mathematics · Three Dimensional Geometry

If the lines $\frac{x - 3}{2} = \frac{y - 5}{2} = \frac{z - 4}{λ}$ and $\frac{x - 2}{λ} = \frac{y - 6}{4} = \frac{z - 5}{2}$ intersect at a point $(α, β, γ)$ , then the greatest value of $λ$ is equal to

Correct answer
A
$0$
B
$2$
C
$- 2$
D
$4$

Solution

Two given lines intersect $\Rightarrow$ they must be coplanar
So, $|\begin{matrix} 3 - 2 & 5 - 6 & 4 - 5 \\ 2 & 2 & λ \\ λ & 4 & 2 \end{matrix}| = 0$

$\Rightarrow 1 (4 - 4 λ) + 1 (4 - λ^{2}) - 1 (8 - 2 λ) = 0$
$\Rightarrow 4 - 4 λ + 4 - λ^{2} - 8 + 2 λ = 0$
$\Rightarrow λ^{2} + 2 λ = 0 \Rightarrow λ = 0, - 2$

Hence, the correct answer is option: 'A'.

If the lines x-32=y-52=z-4λ and x-2λ=y-64=z-52 intersect at a point α,β,γ, then the greatest value of λ is equal to

Solution

More Three Dimensional Geometry Questions

If the lines $\frac{x - 3}{2} = \frac{y - 5}{2} = \frac{z - 4}{λ}$ and $\frac{x - 2}{λ} = \frac{y - 6}{4} = \frac{z - 5}{2}$ intersect at a point $(α, β, γ)$ , then the greatest value of $λ$ is equal to