Ex 11.2, 11 - Class 12 3D Geometry - Find angle between lines - Angle between two lines - Cartisian

Slide27.JPG
Slide28.JPG

Slide29.JPG Slide30.JPG Slide31.JPG

  1. Chapter 11 Class 12 Three Dimensional Geometry
  2. Serial order wise
Ask Download

Transcript

Ex 11.2, 11 Find the angle between the following pairs of lines: (i) 𝑥 − 2﷮2﷯ = 𝑦 − 1﷮5﷯ = 𝑧 + 3﷮−3﷯ and 𝑥 + 2﷮−1﷯ = 𝑦 − 4﷮8﷯ = 𝑧 − 5﷮4﷯ Angle between the pair of lines 𝑥 − 𝑥1﷮𝑎1﷯ = 𝑦 − 𝑦1﷮𝑏1﷯ = 𝑧 − 𝑧1﷮𝑐1﷯ and 𝑥 − 𝑥2﷮𝑎2﷯ = 𝑦 − 𝑦2﷮𝑏2﷯ = 𝑧 − 𝑧2﷮𝑐2﷯ is given by cos θ = 𝒂𝟏𝒂𝟐 + 𝒃𝟏 + 𝒃𝟐 + 𝒄𝟏 + 𝒄𝟐﷮ ﷮𝒂𝟏𝟐 + 𝒃𝟏𝟐 + 𝒄𝟏𝟐﷯ ﷮𝒂𝟐𝟐 + 𝒃𝟐𝟐 + 𝒄𝟐𝟐﷯﷯﷯ = 26﷮ ﷮38﷯ ﷮81﷯﷯﷯ = 26﷮ ﷮38﷯ × 9﷯﷯ = 26﷮9 ﷮38﷯ ﷯ So, cos θ = 26﷮9 ﷮38﷯ ﷯ ∴ θ = cos-1 𝟐𝟔﷮𝟗 ﷮𝟑𝟖﷯ ﷯﷯ Therefore, the angle between the given lines is cos-1 26﷮9 ﷮38﷯ ﷯﷯. Ex 11.2, 11 Find the angle between the following pairs of lines: (ii) 𝑥﷮2﷯ = 𝑦﷮2﷯ = 𝑧﷮1﷯ and 𝑥 − 5﷮4﷯ = 𝑦 − 2﷮1﷯ = 𝑧 − 3﷮8﷯ Angle between the pair of lines 𝑥 − 𝑥1﷮𝑎1﷯ = 𝑦 − 𝑦1﷮𝑏1﷯ = 𝑧 − 𝑧1﷮𝑐1﷯ and 𝑥 − 𝑥2﷮𝑎2﷯ = 𝑦 − 𝑦2﷮𝑏2﷯ = 𝑧 − 𝑧2﷮𝑐2﷯ is given by cos θ = 𝒂𝟏𝒂𝟐 + 𝒃𝟏 + 𝒃𝟐 + 𝒄𝟏 + 𝒄𝟐﷮ ﷮𝒂𝟏𝟐 + 𝒃𝟏𝟐 + 𝒄𝟏𝟐﷯ ﷮𝒂𝟐𝟐 + 𝒃𝟐𝟐 + 𝒄𝟐𝟐﷯﷯﷯ = 18﷮ ﷮9﷯ × ﷮81﷯﷯﷯ = 18﷮3 × 9﷯ = 2﷮3﷯ So, cos θ = 2﷮3﷯ ∴ θ = cos-1 𝟐﷮𝟑﷯﷯ Therefore, the angle between the given lines is cos-1 2﷮3﷯﷯.

About the Author

Davneet Singh's photo - Teacher, Computer Engineer, Marketer
Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.