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, 2 Important
Example, 3
Example, 4 Important
Example, 5 Important
Example, 6 Important
Example, 7
Example 8
Example, 9 Deleted for CBSE Board 2021 Exams only
Example 10 Deleted for CBSE Board 2021 Exams only
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 2021 Exams only
Example 23 Important Deleted for CBSE Board 2021 Exams only You are here
Example 24
Example, 25 Important
Example 26
Example 27 Important
Example 28 Important
Example 29 Important
Example 30 Important
Examples
About the Author