Check sibling questions

Example 9 - Find angle between pair of lines r = 3i+2j-4k - Angle between two lines - Vector

Example, 9 - Chapter 11 Class 12 Three Dimensional Geometry - Part 2
Example, 9 - Chapter 11 Class 12 Three Dimensional Geometry - Part 3

Get live Maths 1-on-1 Classs - Class 6 to 12


Transcript

Example, 9 Find the angle between the pair of lines given by 𝑟﷯ = 3 𝑖﷯ + 2 𝑗﷯ – 4 𝑘﷯ + 𝜆 ( 𝑖﷯ + 2 𝑗﷯ + 2 𝑘﷯) and 𝑟﷯ = 5 𝑖﷯ – 2 𝑗﷯ + 𝜇(3 𝑖﷯ + 2 𝑗﷯ + 6 𝑘﷯) Angle between two line 𝑟﷯ = 𝑎1﷯ + 𝜆 𝑏1﷯ & 𝑟﷯ = 𝑎2﷯ + 𝜇 𝑏2﷯ is given by cos θ = 𝑏1﷯ . 𝑏2﷯﷮ 𝑏1﷯﷯ 𝑏2﷯﷯﷯﷯ Given, the pair of lines is Now, 𝑏1﷯ . 𝑏2﷯ = (1 𝑖﷯ + 2 𝑗﷯ + 2 𝑘﷯). (3 𝑖﷯ + 2 𝑗﷯ + 6 𝑘﷯) = (1 × 3) + (2 × 2) + (2 × 6) = 3 + 4 + 12 = 19 Magnitude of 𝑏1﷯ = ﷮12 + 22 + 22﷯ 𝑏1﷯﷯ = ﷮1 + 4 + 4﷯ = ﷮9﷯ = 3 Magnitude of 𝑏2﷯ = ﷮32 + 22 + 62﷯ 𝑏2﷯﷯ = ﷮9 + 4 + 36﷯ = ﷮49﷯ = 7 Now, cos θ = 𝑏1﷯. 𝑏2﷯﷮ 𝑏1﷯﷯ 𝑏2﷯﷯﷯﷯ cos θ = 19﷮3 × 7 ﷯﷯ cos θ = 19﷮21﷯ ∴ θ = cos-1 𝟏𝟗﷮𝟐𝟏﷯﷯ Therefore, the angle between the pair of lines is cos-1 19﷮21﷯﷯

Ask a doubt
Davneet Singh's photo - Co-founder, Teachoo

Made by

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.