Ex 10.4

Chapter 10 Class 12 Vector Algebra
Serial order wise

### Transcript

Ex 10.4, 5 Find λ and μ if (2𝑖 ̂ + 6𝑗 ̂ + 27𝑘 ̂) × (𝑖 ̂ + 𝜆j ̂ + μ𝑘 ̂) = 0 ⃗ Let 𝑎 ⃗ = 2𝑖 ̂ + 6𝑗 ̂ + 27𝑘 ̂ & 𝑏 ⃗ = 1𝑖 ̂ + 𝜆j ̂ + μ𝑘 ̂ Given, 𝑎 ⃗ × 𝑏 ⃗ = 𝑎 ⃗ × 𝑏 ⃗ = |■8(𝑖 ̂&𝑗 ̂&𝑘 ̂@█(2@1)&█(6@"𝜆" )&█(27@"μ" ))| = 𝑖 ̂ [(6×"μ" )−("𝜆" ×27)] − 𝑗 ̂ [(2×"μ" )−(1×27) ] + 𝑘 ̂[(2×"𝜆" )−(1×6)] = 𝑖 ̂ [6"μ" −27"𝜆" ] − 𝑗 ̂ [2"μ" −27 ] + 𝑘 ̂[(2"𝜆" −6)] ∴ 𝑎 ⃗ × 𝑏 ⃗ = [6"μ" −27"𝜆" ] 𝑖 ̂ − (2"μ"−27) 𝑗 ̂ + (2"𝜆" − 6) 𝑘 ̂ Also, 𝑎 ⃗ × 𝑏 ⃗ = 0 ⃗ [𝟔"μ" −𝟐𝟕"𝜆" ] 𝒊 ̂ − (𝟐"μ"−𝟐𝟕) 𝒋 ̂ + (2"𝜆" − 6) 𝒌 ̂ = 0𝒊 ̂ + 0𝒋 ̂ + 0𝒌 ̂ Comparing components Therefore, "𝜆" = 3 and "μ" = 𝟐𝟕/𝟐 𝒊 ̂ 6"μ" − 27"𝜆" = 0 6"μ" − 27"𝜆" "μ" = 27/6 "𝜆" 𝒋 ̂ − (2"μ" − 27) = 0 2"μ" − 27 = 0 2"μ" = 27 "μ" = 27/2 𝒌 ̂ (2"𝜆" − 6) = 0 2"𝜆" = 6 "𝜆" = 3

#### Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.