Question 14 (b) - Plane - Chapter 11 Class 12 Three Dimensional Geometry

Last updated at December 16, 2024 by

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Ex 11.3, 14 (b) - Find distance of (3, -2, 1) from plane 2x-y+2z+3=0

Ex 11.3, 14 (b) - Chapter 11 Class 12 Three Dimensional Geometry - Part 2

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Question 14 In the following cases, find the distance of each of the given points from the corresponding given plane. The distance of the point (x1, y1, z1) from the plane Ax + By + Cz = D is |(š‘Øš’™_šŸ + 怖š‘©š’šć€—_šŸ +怖 š‘Ŗš’›ć€—_šŸ āˆ’ š‘«)/āˆš(š‘Ø^šŸ + š‘©^šŸ + š‘Ŗ^šŸ )| Given, the point is (3, āˆ’2, 1) So, š‘„_1 = 3, š‘¦_1 = āˆ’2, š‘§_1 = 1 a And the equation of the plane is 2x āˆ’ y + 2z + 3 = 0 2x āˆ’ y + 2z = āˆ’3 āˆ’(2x āˆ’ y + 2z) = 3 āˆ’2x + y āˆ’ 2z = 3 Comparing with Ax + By + Cz = D, A = āˆ’2, B = 1, C = āˆ’2, D = 3 Now, Distance of the point form the plane = |((āˆ’2 Ɨ 3) + (1 Ɨ āˆ’2) + (āˆ’2 Ɨ 1) āˆ’ 3)/āˆš((āˆ’2)^2 + 1^2 + (2)^2 )| = |((āˆ’6) + (āˆ’2) + (āˆ’2) āˆ’ 3)/āˆš(4 + 1 + 4)| = |(āˆ’13)/āˆš9| = |(āˆ’13)/3| = šŸšŸ‘/šŸ‘

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