Question

Find the coordinates of points on line `x/1 = (y - 1)/2 = (z + 1)/2` which are at a distance of `sqrt(11)` units from origin.

Answer 1

Given line is

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

x = k, y = 2k + 1, z = 2k – 1

So, let point on the given line is

P(k, 2k + 1, 2k – 1)

Distance of point (P) from the origin is

`sqrt((k - 0)^2 + (2k + 1 - 0)^2 + (2k - 1 - 0)^2`

Now `sqrt(k^2 + (2k + 1)^2 + (2k - 1)^2) = sqrt(11)` ...(Given)

`\implies` k² + 4k² + 1 + 4k + 4k² + 1 – 4k = 11

`\implies` 9k² + 2 = 11

`\implies` 9k² = 9

`\implies` k = ± 1 

Therefore, point on the line is (1, 3, 1) or (– 1, – 1 – 3).