Ex 11.3, 1 - Chapter 11 Class 12 Three Dimensional Geometry - Part 6

Advertisement

Ex 11.3, 1 - Chapter 11 Class 12 Three Dimensional Geometry - Part 7

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. (c) 2x + 3y โ€“ z = 5 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 2x + 3y โˆ’ z = 5 2x + 3y โˆ’ 1z = 5 Comparing with ax + by + cz = d a = 2, b = 3, c = โ€“1 & d = 5 & โˆš(๐‘Ž^2+๐‘^2+๐‘^2 ) = โˆš(2^2 + 3^2 + ใ€–(โˆ’1)ใ€—^2 ) = โˆš(4+9+1) = โˆš14 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 = 2/โˆš14, m = 3/โˆš14, n = ( โˆ’ 1)/โˆš14 โˆด Direction cosines of the normal to the plane are = (๐Ÿ/โˆš๐Ÿ๐Ÿ’, ๐Ÿ‘/โˆš๐Ÿ๐Ÿ’, ( โˆ’๐Ÿ)/โˆš๐Ÿ๐Ÿ’) And, Distance form the origin = ๐‘‘/โˆš(๐‘Ž^2 + ๐‘^2 +ใ€– ๐‘ใ€—^2 ) = ๐Ÿ“/โˆš๐Ÿ๐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.