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

Transcript

Ex 10.4, 5 Find Ξ» and ΞΌ if (2𝑖 Μ‚ + 6𝑗 Μ‚ + 27π‘˜ Μ‚) Γ— (𝑖 Μ‚ + πœ†j Μ‚ + ΞΌπ‘˜ Μ‚) = 0 βƒ— Let π‘Ž βƒ— = 2𝑖 Μ‚ + 6𝑗 Μ‚ + 27π‘˜ Μ‚ & 𝑏 βƒ— = 1𝑖 Μ‚ + πœ†j Μ‚ + ΞΌπ‘˜ Μ‚ Given, π‘Ž βƒ— Γ— 𝑏 βƒ— = π‘Ž βƒ— Γ— 𝑏 βƒ— = |β– 8(𝑖 Μ‚&𝑗 Μ‚&π‘˜ Μ‚@β–ˆ(2@1)&β–ˆ(6@"πœ†" )&β–ˆ(27@"ΞΌ" ))π‘Ž| = 𝑖 Μ‚ [(6Γ—"ΞΌ" )βˆ’("πœ†" Γ—27)] βˆ’ 𝑗 Μ‚ [(2Γ—"ΞΌ" )βˆ’(1Γ—27) ]+ π‘˜ Μ‚[(2Γ—"πœ†" )βˆ’(1Γ—6)] = 𝑖 Μ‚ [6"ΞΌ" βˆ’27"πœ†" ] βˆ’ 𝑗 Μ‚ [2"ΞΌ" βˆ’27 ] + π‘˜ Μ‚[(2"πœ†" βˆ’6)] ∴ π‘Ž βƒ— Γ— 𝑏 βƒ— = [6"ΞΌ" βˆ’27"πœ†" ] 𝑖 Μ‚ βˆ’ (2"ΞΌ"βˆ’27) 𝑗 Μ‚ + (2"πœ†" βˆ’ 6) π‘˜ Μ‚ Also, π‘Ž βƒ— Γ— 𝑏 βƒ— = 0 βƒ— [πŸ”"ΞΌ" βˆ’πŸπŸ•"πœ†" ] π’Š Μ‚ βˆ’ (𝟐"ΞΌ"βˆ’πŸπŸ•) 𝒋 Μ‚ + (2"πœ†" βˆ’ 6) π’Œ Μ‚ = 0π’Š Μ‚ + 0𝒋 Μ‚ + 0π’Œ Μ‚ Comparing components Therefore, "πœ†" = 3 and "ΞΌ" = πŸπŸ•/𝟐 π’Š Μ‚ 6"ΞΌ" βˆ’ 27"πœ†" = 0 6"ΞΌ" βˆ’ 27"πœ†" "ΞΌ" = 27/6 "πœ†" 𝒋 Μ‚ βˆ’ (2"ΞΌ" βˆ’ 27) = 0 2"ΞΌ" βˆ’ 27 = 0 2"ΞΌ" = 27 "ΞΌ" = 27/2 π’Œ Μ‚ (2"πœ†" βˆ’ 6) = 0 2"πœ†" = 6 "πœ†" = 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.