Maharashtra State BoardHSC Arts 12th Board Exam
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Find the Distance of the Point (1, 2, –1) from the Plane X - 2y + 4z - 10 = 0 . - Mathematics and Statistics

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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

Concept: Distance of a Point from a Plane
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