Question

Choose correct alternatives:

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

• `(11)/(4)`

• `-(11)/(4)`

• `(11)/(2)`

• `(4)/(11)`

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))`.

Eplanation:

`x/3 = y/4 = z => (3,4,1)`

`(x-1)/k = (y+2)/3 = (z-3)/(k-1) = (k, 3, k-1)`

(3, 4, 1) × (k, 3, k − 1) = 0

3k + 4 ⋅ 3 + 1 ⋅ (k − 1) = 0

3k + 12 + k − 1 = 0

4k + 11 = 0 ⇒ k

= `(-11)/4`