Ex 11.3, 1 - Chapter 11 Class 12 Three Dimensional Geometry - Part 8

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Ex 11.3, 1 - Chapter 11 Class 12 Three Dimensional Geometry - Part 9

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Ex 11.3, 1 - Chapter 11 Class 12 Three Dimensional Geometry - Part 10

  1. Chapter 11 Class 12 Three Dimensional Geometry (Term 2)
  2. Serial order wise

Transcript

Ex 11.3, 1 In each of the following cases, determine the direction cosines of the normal to the plane and the distance from the origin. (d) 5y + 8 = 0 For plane ax + by + cz = d Direction ratios of normal = a, b, c Direction cosines : l = ๐‘Ž/โˆš(๐‘Ž^2 + ๐‘^2 +ใ€– ๐‘ใ€—^2 ) , m = ๐‘/โˆš(๐‘Ž^2 + ๐‘^2 + ๐‘^2 ) , n = ๐‘/โˆš(๐‘Ž^2 + ๐‘^2 + ๐‘^2 ) Distance from origin = ๐‘‘/โˆš(๐‘Ž^2 + ๐‘^2 + ๐‘^2 ) Given, equation of the plane is 5y + 8 = 0 5y = โˆ’8 โˆ’5y = 8 0x โˆ’ 5y + 0z = 8 0x โˆ’ 5y + 0z = 8 Comparing with ax + by + cz = d a = 0, b = โ€“5, c = 0 & d = 8 & โˆš(๐‘Ž^2+๐‘^2+๐‘^2 ) = โˆš(0^2 + ใ€–(โˆ’5)ใ€—^2 + 0^2 ) = โˆš25 = 5 Direction cosines of the normal to the plane are l = ๐‘Ž/โˆš(๐‘Ž^2 + ๐‘^2 + ๐‘^2 ) , m = ๐‘/โˆš(๐‘Ž^2 + ๐‘^2 + ๐‘^2 ) , n = ๐‘/โˆš(๐‘Ž^2 + ๐‘^2 + ๐‘^2 ) l = 0/5, m = (โˆ’5)/5, n = ( 0)/5 โˆด Direction cosines of the normal to the plane are = (0, โ€“1, 0) And, Distance form the origin = ๐‘‘/โˆš(๐‘Ž^2 + ๐‘^2 + ๐‘^2 ) = ๐Ÿ–/๐Ÿ“

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.