Question

If the line `x/(-3) = "y"/2 = "z"/5` is perpendicular to the line `(x - 2)/2 = ("y - 1")/"k" = ("z - 3")/("k + 11")`, then the value of k is ______.

Options

• - 5

• 7

• - 7

• `1/5`

Answer 1

If the line `x/(-3) = "y"/2 = "z"/5` is perpendicular to the line `(x - 2)/2 = ("y - 1")/"k" = ("z - 3")/("k + 11")`, then the value of k is - 7.

Explanation:

Here, a₁ = - 3, b₁ = 2, c₁ = 5

a₂ = 2, b₂ = k, c₂ = k + 11

Since the given lines are perpendicular,

a₁a₂ + b₁b₂ + c₁c₂ = 0

⇒ (- 3)(2) + 2k + 5(k + 11) = 0

⇒ 7k = - 49

⇒ k = - 7