Question

The co-ordinates of a point on the line x = 4y + 5, z = 3y – 6 at a distance `3sqrt(26)` from the point (5, 0, –6) are ______.

Options

• (17, 3, 3)

• (– 7, 3, –15)

• (–17, –3, –3)

• (7, –3, 15)

Answer 1

The co-ordinates of a point on the line x = 4y + 5, z = 3y – 6 at a distance `3sqrt(26)` from the point (5, 0, –6) are (17, 3, 3).

Explanation:

The given equation of line is

x = 4y + 5, z = 3y – 6.

It can be written as

`(x - 5)/4 = y = (z + 6)/3` = r, say

∴ Co-ordinates of the any point on the line are (4r + 5, 3r – 6).

This point is at a distance of `3sqrt(26)` from the point (5, 0, –6)

 ∴ (4r + 5 – 5)² + (r – 0)² + (3r – 6 + 6)² = `(3sqrt(26))^2`

⇒ 16r² + r² + 9r² = 234

⇒ 26r² = 234

⇒ r² = 9

⇒ r = `+- 3`

If r = 3, then the point is

(4 x 3 + 5, 3, 3 x 3 – 6) = (17, 3, 3)