Question

The lines `(x - 2)/1 = (y - 3)/1 = (4 - z)/k` and `(x - 1)/k = (y - 4)/2 = (z - 5)/(-2)` are mutually perpendicular if the value of k is ______.

Options

• `- 2/3`

• `2/3`

• – 2

• 2

Answer 1

The lines `(x - 2)/1 = (y - 3)/1 = (4 - z)/k` and `(x - 1)/k = (y - 4)/2 = (z - 5)/(-2)` are mutually perpendicular if the value of k is 2.

Explanation:

If `(x - 2)/1 = (y - 3)/1 = (z - 4)/(-k)`

And `(x - 1)/k = (y - 4)/2 = (z - 5)/(-2)` are perpendicular then

1 × k + 1 × 2 + (k) × (–2) = 0

⇒ k + 2 + 2k = 0

⇒ 2 + 3k = 0

⇒ k = `- 2/3`