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  1. Chapter 10 Class 12 Vector Algebra
  2. Serial order wise

Transcript

Example 14 Find angle β€˜ΞΈβ€™ between the vectors π‘Ž βƒ— = 𝑖 Μ‚ + 𝑗 Μ‚ βˆ’ π‘˜ Μ‚ and 𝑏 βƒ— =𝑖 Μ‚ βˆ’ 𝑗 Μ‚ + π‘˜ Μ‚. π‘Ž βƒ— = 𝑖 Μ‚ + 𝑗 Μ‚ βˆ’ π‘˜ Μ‚ = 1𝑖 Μ‚ + 1𝑗 Μ‚ βˆ’ 1π‘˜ Μ‚ 𝑏 βƒ— = 𝑖 Μ‚ – 𝑗 Μ‚ + π‘˜ Μ‚ = 1𝑖 Μ‚ βˆ’ 1𝑗 Μ‚ + 1π‘˜ Μ‚ Magnitude of π‘Ž βƒ— = √(12+1^2+(βˆ’1)2) |π‘Ž βƒ— | = √(1+1+1) = √3 Magnitude of 𝑏 βƒ— = √(12+(βˆ’1)2+12) |𝑏 βƒ— | = √(1+1+1) = √3 We know that , π‘Ž βƒ— .𝑏 βƒ— = |π‘Ž βƒ— | |𝑏 βƒ— | cosΞΈ 𝒂 βƒ— .𝒃 βƒ— = (1𝑖 Μ‚ + 1𝑗 Μ‚ – 1π‘˜ Μ‚). (1𝑖 Μ‚ βˆ’ 1𝑗 Μ‚ + 1π‘˜ Μ‚) = 1.1 + 1.(βˆ’1) + (βˆ’1)1 = 1 – 1 βˆ’ 1 = βˆ’1 Now, π‘Ž βƒ— .𝑏 βƒ— = √3 Γ— √3 Γ— cos ΞΈ βˆ’1 = 3 cos ΞΈ cos ΞΈ = (βˆ’1)/3 ΞΈ = cosβˆ’1 ((βˆ’πŸ)/πŸ‘) Therefore, the angle between π‘Ž βƒ— and 𝑏 βƒ— is cos-1((βˆ’1)/3)

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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.