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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.
Solution
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
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