Check sibling questions

Example 17 - Find |a - b|, if |a| = 2|b| = 3 and a.b = 4

Example 17 - Chapter 10 Class 12 Vector Algebra - Part 2

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Example 17 Find |π‘Ž βƒ— βˆ’ 𝑏 βƒ—| , if two vectors a and b are such that |π‘Ž βƒ—| = 2, |𝑏 βƒ—| = 3 and π‘Ž βƒ— β‹… 𝑏 βƒ— = 4. Given, |𝒂 βƒ— | = 2 , |𝒃 βƒ— | = 2 & 𝒂 βƒ—. 𝒃 βƒ— = 4 We need to find |π‘Ž βƒ—βˆ’π‘ βƒ— | Taking square, |𝒂 βƒ—βˆ’π’ƒ βƒ— |2 = (𝒂 βƒ—βˆ’π’ƒ βƒ—). (𝒂 βƒ—βˆ’π’ƒ βƒ—) = π‘Ž βƒ— . π‘Ž βƒ— βˆ’ π‘Ž βƒ— . 𝑏 βƒ— βˆ’ 𝒃 βƒ—. 𝒂 βƒ— + 𝑏 βƒ— . 𝑏 βƒ— = π‘Ž βƒ— . π‘Ž βƒ— βˆ’ π‘Ž βƒ— . 𝑏 βƒ— βˆ’ 𝒂 βƒ— . 𝒃 βƒ— + 𝑏 βƒ— . 𝑏 βƒ— = 𝒂 βƒ—. 𝒂 βƒ— βˆ’ 2π‘Ž βƒ— . 𝑏 βƒ— + 𝒃 βƒ—. 𝒃 βƒ— = |𝒂 βƒ— |2 βˆ’ 2π‘Ž βƒ—. 𝑏 βƒ— + |𝒃 βƒ— |2 = 22 – 2 Γ— 4 + 32 = 4 βˆ’ 8 + 9 = 5 Thus, |𝒂 βƒ—βˆ’π’ƒ βƒ— |2 = 5 |π‘Ž βƒ—βˆ’π‘ βƒ— | = Β± √5 Since magnitude is not negative, So, |𝒂 βƒ—βˆ’π’ƒ βƒ— | = βˆšπ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 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.