Question

If the line `x/(3) = y/(4)` = z is perpendicular to the line `(x - 1)/k = (y + 2)/(3) = (z - 3)/(k - 1)`, then the value of k is ______.

Options

• -5

• 7

• -7

• `(-11)/4`

Answer 1

If the line `x/(3) = y/(4)` = z is perpendicular to the line `(x - 1)/k = (y + 2)/(3) = (z - 3)/(k - 1)`, then the value of k is `underline((-11)/4)`.

Explanation:

Here,

a₁ = 3, b₁ = 4, c₁ = 1

a₂ = k, b₂ = 3, c₂ = k - 1

Since the given lines are perpendicular,

a₁a₂ + b₁b₂ + c₁c₂ = 0

⇒ 3k + 12 + k - 1 = 0

⇒ 4k = -11

`=> k = (-11)/4`