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Example 22 - Find |a x b|, if a=2i+j+3k and b=3i+5j-2k - Examples

Example 22 - Chapter 10 Class 12 Vector Algebra - Part 2

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Example 22 Find |π‘Ž βƒ— Γ— 𝑏 βƒ—|, if π‘Ž βƒ— = 2𝑖 Μ‚ + 𝑗 Μ‚ + 3π‘˜ Μ‚ and 𝑏 βƒ— = 3𝑖 Μ‚ + 5𝑗 Μ‚ βˆ’ 2π‘˜ Μ‚ Given 𝒂 βƒ— = 2𝑖 Μ‚ + 𝑗 Μ‚ + 3π‘˜ Μ‚ 𝒃 βƒ— = 3𝑖 Μ‚ + 5𝑗 Μ‚ βˆ’ 2π‘˜ Μ‚ Now, 𝒂 βƒ— Γ— 𝒃 βƒ— = |β– 8(𝑖 Μ‚&𝑗 Μ‚&π‘˜ Μ‚@2&1&3@3&5&βˆ’2)| = 𝑖 Μ‚ (1 Γ— (-2) – 5 Γ— 3) βˆ’ 𝑗 Μ‚ (2 Γ— (-2) βˆ’ 3 Γ— 3) + π‘˜ Μ‚ (2 Γ— 5 βˆ’ 3 Γ— 1) = 𝑖 Μ‚ (βˆ’2 βˆ’15) βˆ’ 𝑗 Μ‚ (βˆ’4 βˆ’9) + π‘˜ Μ‚ (10 βˆ’ 3) = –17π’Š Μ‚ + 13𝒋 Μ‚ + 7π’Œ Μ‚ So, Magnitude of π‘Ž βƒ— Γ— 𝑏 βƒ— = √((βˆ’17)2+(13)2+(7)2) |π‘Ž βƒ—" Γ— " 𝑏 βƒ— | = √(289+169+49) = √507 Thus, |π‘Ž βƒ—" Γ— " 𝑏 βƒ— | = βˆšπŸ“πŸŽπ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.