Ex 10.3, 2 - Find angle between vectors i - 2j + 3k, 3i - 2j + k

Ex 10.3, 2 - Chapter 10 Class 12 Vector Algebra - Part 2
Ex 10.3, 2 - Chapter 10 Class 12 Vector Algebra - Part 3

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Transcript

Ex 10.3, 2 Find the angle between the vectors 𝑖 Μ‚ βˆ’ 2𝑗 Μ‚ + 3π‘˜ Μ‚ and 3𝑖 Μ‚ - 2𝑗 Μ‚ + π‘˜ Μ‚Let π‘Ž βƒ— = 𝑖 Μ‚ βˆ’ 2𝑗 Μ‚ + 3π‘˜ Μ‚ = 1𝑖 Μ‚ βˆ’ 2𝑗 Μ‚ + 3π‘˜ Μ‚ and 𝑏 βƒ— = 3𝑖 Μ‚ βˆ’ 2𝑗 Μ‚ + π‘˜ Μ‚ = 3𝑖 Μ‚ βˆ’ 2𝑗 Μ‚ + 1π‘˜ Μ‚ We know that π‘Ž βƒ— . 𝑏 βƒ— = |π‘Ž βƒ— ||𝑏 βƒ— | cos ΞΈ ; ΞΈ is the angle between π‘Ž βƒ— & 𝑏 βƒ— Now, 𝒂 βƒ—. 𝒃 βƒ— = (1𝑖 Μ‚ βˆ’ 2𝑗 Μ‚ + 3π‘˜ Μ‚). (3𝑖 Μ‚ βˆ’ 2𝑗 Μ‚ + 1π‘˜ Μ‚) = 1.3 + (βˆ’2).(βˆ’2) + 3.1 = 3 + 4 + 3 = 10 Magnitude of π‘Ž βƒ— = √(12+(βˆ’2)2+32) |π‘Ž βƒ— |= √(1+4+9) = √14 Magnitude of 𝑏 βƒ— = √(32+(βˆ’2)2+12) |𝑏 βƒ— |= √(9+4+1) = √14 Now, π‘Ž βƒ— . 𝑏 βƒ— = |π‘Ž βƒ— ||𝑏 βƒ— | cos ΞΈ 10 = √14 Γ— √14 x cos ΞΈ 10 = 14 Γ— cos ΞΈ cos ΞΈ = 10/14 ΞΈ = cos-1(πŸ“/πŸ•) Thus, the angle between π‘Ž βƒ— and 𝑏 βƒ— is cos-1(5/7)

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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.