Question

The equation of line is `(x - 1)/2 = (y + 1)/(-2) = (z + 1)/1`. The co-ordinates of the point on the line at a distance of 3 units from the point (1, -1, -1) is ______ 

Options

• (7, -7, 2)

• (3, -3, 0)

• (6, 7, -2)

• (-3, 3, 0)

Answer 1

The equation of line is `(x - 1)/2 = (y + 1)/(-2) = (z + 1)/1`. The co-ordinates of the point on the line at a distance of 3 units from the point (1, -1, -1) is (3, -3, 0)

Explanation:

Let `(x - 1)/2 = (y + 1)/(-2) = (z + 1)/1 = lambda`

Any point on the line is

P ≡ (2λ + 1, -2λ - 1, λ - 1)

Let A ≡ (1, -1, -1)

Now, PA = 3

∴ `sqrt((2lambda + 1 - 1)^2 + (-2lambda - 1 + 1)^2 + (lambda - 1 + 1)^2) = 3`

⇒ `sqrt(4lambda^2 + 4lambda^2 + lambda^2)` = 3

⇒ `9lambda^2 = 9`

⇒ `lambda = ± 1`

∴ P ≡ (3, -3, 0) or P ≡ (-1, 1, -2)