Last updated at May 29, 2018 by Teachoo

Transcript

Ex 11.2, 11 Find the angle between the following pairs of lines: (i) 𝑥 − 22 = 𝑦 − 15 = 𝑧 + 3−3 and 𝑥 + 2−1 = 𝑦 − 48 = 𝑧 − 54 Angle between the pair of lines 𝑥 − 𝑥1𝑎1 = 𝑦 − 𝑦1𝑏1 = 𝑧 − 𝑧1𝑐1 and 𝑥 − 𝑥2𝑎2 = 𝑦 − 𝑦2𝑏2 = 𝑧 − 𝑧2𝑐2 is given by cos θ = 𝒂𝟏𝒂𝟐 + 𝒃𝟏 + 𝒃𝟐 + 𝒄𝟏 + 𝒄𝟐 𝒂𝟏𝟐 + 𝒃𝟏𝟐 + 𝒄𝟏𝟐 𝒂𝟐𝟐 + 𝒃𝟐𝟐 + 𝒄𝟐𝟐 = 26 38 81 = 26 38 × 9 = 269 38 So, cos θ = 269 38 ∴ θ = cos-1 𝟐𝟔𝟗 𝟑𝟖 Therefore, the angle between the given lines is cos-1 269 38 . Ex 11.2, 11 Find the angle between the following pairs of lines: (ii) 𝑥2 = 𝑦2 = 𝑧1 and 𝑥 − 54 = 𝑦 − 21 = 𝑧 − 38 Angle between the pair of lines 𝑥 − 𝑥1𝑎1 = 𝑦 − 𝑦1𝑏1 = 𝑧 − 𝑧1𝑐1 and 𝑥 − 𝑥2𝑎2 = 𝑦 − 𝑦2𝑏2 = 𝑧 − 𝑧2𝑐2 is given by cos θ = 𝒂𝟏𝒂𝟐 + 𝒃𝟏 + 𝒃𝟐 + 𝒄𝟏 + 𝒄𝟐 𝒂𝟏𝟐 + 𝒃𝟏𝟐 + 𝒄𝟏𝟐 𝒂𝟐𝟐 + 𝒃𝟐𝟐 + 𝒄𝟐𝟐 = 18 9 × 81 = 183 × 9 = 23 So, cos θ = 23 ∴ θ = cos-1 𝟐𝟑 Therefore, the angle between the given lines is cos-1 23.

Chapter 11 Class 12 Three Dimensional Geometry

Example, 3
Important

Ex 11.1, 2 Important

Example, 6 Important

Example, 9 Important

Example 12 Important

Ex 11.2, 5 Important

Ex 11.2, 11 Important You are here

Ex 11.2, 12 Important

Ex 11.2, 14 Important

Ex 11.2, 15 Important

Ex 11.2, 17 Important

Example 20 Important

Example 21 Important

Example 23 Important

Example 24 Important

Example, 25 Important

Ex 11.3, 4 Important

Ex 11.3, 11 Important

Ex 11.3, 12 Important

Ex 11.3, 14 Important

Example 27 Important

Example 29 Important

Example 30 Important

Misc 6 Important

Misc 9 Important

Misc 14 Important

Misc 18 Important

Misc 20 Important

Misc 21 Important

Class 12

Important Question for exams Class 12

- Chapter 1 Class 12 Relation and Functions
- Chapter 2 Class 12 Inverse Trigonometric Functions
- Chapter 3 Class 12 Matrices
- Chapter 4 Class 12 Determinants
- Chapter 5 Class 12 Continuity and Differentiability
- Chapter 6 Class 12 Application of Derivatives
- Chapter 7 Class 12 Integrals
- Chapter 8 Class 12 Application of Integrals
- Chapter 9 Class 12 Differential Equations
- Chapter 10 Class 12 Vector Algebra
- Chapter 11 Class 12 Three Dimensional Geometry
- Chapter 12 Class 12 Linear Programming
- Chapter 13 Class 12 Probability

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.