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

Last updated at Dec. 16, 2024 by Teachoo

 

 

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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 |(๐‘จ๐’™_๐Ÿ + ใ€–๐‘ฉ๐’šใ€—_๐Ÿ +ใ€– ๐‘ช๐’›ใ€—_๐Ÿ โˆ’ ๐‘ซ)/โˆš(๐‘จ^๐Ÿ + ๐‘ฉ^๐Ÿ + ๐‘ช^๐Ÿ )| Given, the point is (3, โˆ’2, 1) So, ๐‘ฅ_1 = 3, ๐‘ฆ_1 = โˆ’2, ๐‘ง_1 = 1 a And the equation of the plane is 2x โˆ’ y + 2z + 3 = 0 2x โˆ’ y + 2z = โˆ’3 โˆ’(2x โˆ’ y + 2z) = 3 โˆ’2x + y โˆ’ 2z = 3 Comparing with Ax + By + Cz = D, A = โˆ’2, B = 1, C = โˆ’2, D = 3 Now, Distance of the point form the plane = |((โˆ’2 ร— 3) + (1 ร— โˆ’2) + (โˆ’2 ร— 1) โˆ’ 3)/โˆš((โˆ’2)^2 + 1^2 + (2)^2 )| = |((โˆ’6) + (โˆ’2) + (โˆ’2) โˆ’ 3)/โˆš(4 + 1 + 4)| = |(โˆ’13)/โˆš9| = |(โˆ’13)/3| = ๐Ÿ๐Ÿ‘/๐Ÿ‘
  1. Chapter 11 Class 12 Three Dimensional Geometry
  2. Serial order wise

    3. Plane

    Direction cosines and ratios →
Direction cosines and ratios →
Chapter 11 Class 12 Three Dimensional Geometry
Serial order wise

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo