Last updated at May 29, 2018 by Teachoo

Transcript

Ex 11.3, 12 Find the angle between the planes whose vector equations are 𝑟 . (2 𝑖 + 2 𝑗 – 3 𝑘) = 5 and 𝑟 . (3 𝑖 – 3 𝑗 + 5 𝑘) = 3 . Angle between two planes 𝑟 . 𝑛1 = d1 and 𝑟. 𝑛2 = d2 is given by cos 𝜃 = 𝒏𝟏. 𝒏𝟐 𝒏𝟏 𝒏𝟐 Given, the two planes are So, cos θ = 2 𝑖 + 2 𝑗 − 3 𝑘 . 3 𝑖 − 3 𝑗 + 5 𝑘 17 × 43 = 2 × 3 + 2 × −3 + (−3 × 5) 17 × 43 = 6 − 6 − 15 731 = −15 731 = 15 731 So, cos θ = 15 731 ∴ θ = cos−1 𝟏𝟓 𝟕𝟑𝟏 Therefore, the angle between the planes is cos−1 15 731.

Chapter 11 Class 12 Three Dimensional Geometry

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 9 years. He provides courses for Maths and Science at Teachoo.