Find the Distance of the Point (1, 2, –1) from the Plane X - 2y + 4z - 10 = 0 . - Mathematics and Statistics

प्रश्न

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

उत्तर

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

D = $| \frac{a x_{1} + b y_{1} + c z_{1} + d}{\sqrt{a^{2} + b^{2} + c^{2}}} |$

:. (x₁y₁z₁) ≡ (1,2,-1)

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

$∴ D = | \frac{1 - 2 (2) + 4 (- 1) - 10}{\sqrt{1 + 4 + 16}} | = | \frac{- 17}{\sqrt{21}} | = \frac{17}{\sqrt{21}}$ units

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Distance of a Point from a Plane

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Q 1.2.3 Q 1.2.2 Q 1.2.4

2017-2018 (March)

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2017-2018 (March) (with solutions)

Q 1.2.3 | 2 marks

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Distance of a Point from a Plane

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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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