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