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Ex 11.2, 11 - Chapter 11 Class 12 Three Dimensional Geometry - Part 4

Ex 11.2, 11 - Chapter 11 Class 12 Three Dimensional Geometry - Part 5
Ex 11.2, 11 - Chapter 11 Class 12 Three Dimensional Geometry - Part 6

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Transcript

Angle between the pair of lines (π‘₯ βˆ’ π‘₯1)/π‘Ž1 = (𝑦 βˆ’ 𝑦1)/𝑏1 = (𝑧 βˆ’ 𝑧1)/𝑐1 and (π‘₯ βˆ’ π‘₯2)/π‘Ž2 = (𝑦 βˆ’ 𝑦2)/𝑏2 = (𝑧 βˆ’ 𝑧2)/𝑐2 is given by cos ΞΈ = |(𝒂_𝟏 𝒂_𝟐 + 𝒃_𝟏 𝒃_𝟐 +γ€– 𝒄〗_𝟏 𝒄_𝟐)/(√(〖𝒂_πŸγ€—^𝟐 + 〖𝒃_πŸγ€—^𝟐+ 〖𝒄_πŸγ€—^𝟐 ) √(〖𝒂_πŸγ€—^𝟐 +γ€–γ€– 𝒃〗_πŸγ€—^𝟐+ 〖𝒄_πŸγ€—^𝟐 ))| 𝒙/𝟐 = π’š/𝟐 = 𝒛/𝟏 (π‘₯ βˆ’ 0)/2 = (𝑦 βˆ’ 0)/2 = (𝑧 βˆ’ 0)/1 Comparing with (π‘₯ βˆ’ π‘₯1)/π‘Ž1 = (𝑦 βˆ’ 𝑦1)/𝑏1 = (𝑧 βˆ’ 𝑧1)/𝑐1 x1 = 0, y1 = 0, z1 = 0 & π‘Ž1 = 2, b1 = 2, c1 = 1 (𝒙 βˆ’ πŸ“)/πŸ’ = (π’š βˆ’ 𝟐)/𝟏 = (𝒛 βˆ’ πŸ“)/πŸ– Comparing with (π‘₯ βˆ’ π‘₯2)/π‘Ž2 = (𝑦 βˆ’ 𝑦2)/𝑏2 = (𝑧 βˆ’ 𝑧2)/𝑐2 π‘₯2 = 5, y2 = 2, z2 = 5 & π‘Ž2 = 4, 𝑏2 = 1, 𝑐2 = 8 Now, cos ΞΈ = |(𝒂_𝟏 𝒂_𝟐 + 𝒃_𝟏 𝒃_𝟐 +γ€– 𝒄〗_𝟏 𝒄_𝟐)/(√(〖𝒂_πŸγ€—^𝟐 + 〖𝒃_πŸγ€—^𝟐+ 〖𝒄_πŸγ€—^𝟐 ) √(〖𝒂_πŸγ€—^𝟐 +γ€–γ€– 𝒃〗_πŸγ€—^𝟐+ 〖𝒄_πŸγ€—^𝟐 ))| = |((2 Γ— 4) + (2 Γ— 1) + (1 Γ— 8) )/(√(22 + 22 + 12) Γ— √(42 + 12 + 82))| = |(8 + 2 + 8 )/(√(4 + 4 + 1) √(16 + 1 + 64))| = |18/(√9 Γ— √81)| = 18/(3 Γ— 9) = 2/3 So, cos ΞΈ = 2/3 ∴ ΞΈ = cos-1 (𝟐/πŸ‘) Therefore, the angle between the given lines is cosβˆ’1(𝟐/πŸ‘).

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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.