Question

Find the distance of the point (1, 2, –1) from the plane x - 2y + 4z - 10 = 0 .

Answer 1

The distance of the point  (x₁ y₁ z₁) to plane ax + by + cz + d = 0

D = `|(ax_1 + by_1 + cz_1 + d)/(sqrt(a^2+b^2 + c^2))|`

:. (x₁y₁z₁) ≡ (1,2,-1)

a = 1, b = -2, c = 4

`:. D = |(1-2(2)+4(-1)-10)/(sqrt(1+4+16))| = |(-17)/sqrt(21)| = 17/sqrt(21)` units