Question

If the distance of the point (1, 1, 1) from the plane x – y + z + λ = 0 is `5/sqrt(3)`, find the value(s) of λ.

Answer 1

We know that, distance of (x₁, y₁, z₁) from a plane ax + by + cz + d = 0 is given by p = `|(ax_1 + by_1 + cz_1 + d)/sqrt(a^2 + b^2 + c^2)|`

Given, p = `5/sqrt(3)` and (x₁, y₁, z₁) = (1, 1, 1)

∴ `5/sqrt(3) = |(1 - 1 + 1 + λ)/sqrt(1^2 + 1^2 + 1^2)|`

⇒ `5/sqrt(3) = |(λ + 1)/sqrt(3)|`

⇒ λ + 1 = ±5

⇒ λ = 4 or –6