Ex 11.3, 1 - Chapter 11 Class 12 Three Dimensional Geometry - Part 4

Advertisement

Ex 11.3, 1 - Chapter 11 Class 12 Three Dimensional Geometry - Part 5

Advertisement

  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. (b) x + y + z = 1 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 plane is x + y + z = 1 1x + 1y + 1z = 1 Comparing with ax + by + cz = d a = 1, b = 1, c = 1 & d = 1 & โˆš(๐‘Ž^2+๐‘^2+๐‘^2 ) = โˆš(1^2+1^2+1^2 ) = โˆš3 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 = 1/โˆš3 , m = 1/โˆš3, n = 1/โˆš3 โˆด Direction cosines of the normal to the plane are = (๐Ÿ/โˆš๐Ÿ‘, ๐Ÿ/โˆš๐Ÿ‘, ๐Ÿ/โˆš๐Ÿ‘) And, Distance form the origin = ๐‘‘/โˆš(๐‘Ž^2 + ๐‘^2 + ๐‘^2 ) = ๐Ÿ/โˆš๐Ÿ‘

About the Author

Davneet Singh's photo - Teacher, Engineer, Marketer
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.