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

Serial order wise

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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.