### Advertisement

### Advertisement

Last updated at Feb. 1, 2020 by Teachoo

Transcript

Example 23 Find the angle between the two planes 3x โ 6y + 2z = 7 and 2x + 2y โ 2z =5.Angle between two planes A1x + B1y + C1z = d1 and A2x + B2y + C2z = d2 is given by cos ฮธ = |(๐จ_๐ ๐จ_๐ + ๐ฉ_๐ ๐ฉ_๐ + ๐ช_๐ ๐ช_๐)/(โ(ใ๐จ_๐ใ^๐ + ใ๐ฉ_๐ใ^๐ + ใ๐ช_๐ใ^๐ ) โ(ใ๐จ_๐ใ^๐ + ใ๐ฉ_๐ใ^๐ + ใ๐ช_๐ใ^๐ ))| Given the two planes are 3x โ 6y + 2z = 7 Comparing with A1x + B1y + C1z = d1 A1 = 3 , B1 = โ6 , C1 = 2 , ๐_1= 7 2x + 2y โ 2z = 5 Comparing with A2x + B2y + C2z = d2 A2 = 2 , B2 = 2 , C2 = โ2 , ๐_2= 5 So, cos ฮธ = |((3 ร 2) + (โ6 ร 2) + (2 ร โ2))/(โ(3^2 + ใ(โ6)ใ^2 + 2^2 ) โ(2^2 + 2^2 + ใ(โ2)ใ^2 ))| = |(6 + (โ12) + (โ4))/(โ(9 + 36 + 4) รโ(4 + 4 + 4))| = |(โ10)/(โ(49 ) รโ12)| = |(โ10)/(7 รโ(4ร3))| = 10/(7 ร 2 ร โ3) = 5/(7โ3) = 5/(7โ3) ร โ3/โ3 = (5โ3)/21 So, cos ฮธ = (5โ3)/21 โด ฮธ = ใ๐๐๐ใ^(โ๐) ((๐โ๐)/๐๐) Therefore, the angle between the two planes is ใ๐๐๐ ใ^(โ1) ((5โ3)/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.