Example 23 - Chapter 11 Class 12 Three Dimensional Geometry (Term 2)
Last updated at Feb. 1, 2020 by
Transcript
Example 23 Find the angle between the two planes 3x β 6y + 2z = 7 and 2x + 2y β 2z =5.Angle between two planes A1x + B1y + C1z = d1 and A2x + B2y + C2z = d2 is given by cos ΞΈ = |(π¨_π π¨_π + π©_π π©_π + πͺ_π πͺ_π)/(β(γπ¨_πγ^π + γπ©_πγ^π + γπͺ_πγ^π ) β(γπ¨_πγ^π + γπ©_πγ^π + γπͺ_πγ^π ))| Given the two planes are 3x β 6y + 2z = 7 Comparing with A1x + B1y + C1z = d1 A1 = 3 , B1 = β6 , C1 = 2 , π_1= 7 2x + 2y β 2z = 5 Comparing with A2x + B2y + C2z = d2 A2 = 2 , B2 = 2 , C2 = β2 , π_2= 5 So, cos ΞΈ = |((3 Γ 2) + (β6 Γ 2) + (2 Γ β2))/(β(3^2 + γ(β6)γ^2 + 2^2 ) β(2^2 + 2^2 + γ(β2)γ^2 ))| = |(6 + (β12) + (β4))/(β(9 + 36 + 4) Γβ(4 + 4 + 4))| = |(β10)/(β(49 ) Γβ12)| = |(β10)/(7 Γβ(4Γ3))| = 10/(7 Γ 2 Γ β3) = 5/(7β3) = 5/(7β3) Γ β3/β3 = (5β3)/21 So, cos ΞΈ = (5β3)/21 β΄ ΞΈ = γπππγ^(βπ) ((πβπ)/ππ) Therefore, the angle between the two planes is γπππ γ^(β1) ((5β3)/21) E
Examples
Example 1
Example, 2 Important
Example, 3
Example, 4 Important
Example, 5 Important
Example, 6 Important
Example, 7
Example 8
Example, 9 Deleted for CBSE Board 2022 Exams
Example 10 Important Deleted for CBSE Board 2022 Exams
Example 11
Example 12 Important
Example 13 Important
Example 14
Example 15
Example 16 Important
Example 17
Example 18
Example 19 Important
Example 20 Important
Example 21 Important
Example 22 Deleted for CBSE Board 2022 Exams
Example 23 Important Deleted for CBSE Board 2022 Exams You are here
Example 24
Example, 25 Important Deleted for CBSE Board 2022 Exams
Example 26
Example 27 Important
Example 28 Important
Example 29 Important
Example 30 Important
Chapter 11 Class 12 Three Dimensional Geometry (Term 2)
Serial order wise
About the Author
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.
