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Chapter 11 Class 12 Three Dimensional Geometry

Serial order wise

Last updated at March 22, 2023 by Teachoo

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 = 193 × 7 cos θ = 1921 ∴ θ = cos-1 𝟏𝟗𝟐𝟏 Therefore, the angle between the pair of lines is cos-1 1921