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Find λ and μ if (2i + 6j + 27k) x (i + λj + μk) = 0 [Video]

Ex 10.4, 5 - Chapter 10 Class 12 Vector Algebra - Part 2


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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 ̂@█([email protected])&█([email protected]"𝜆" )&█([email protected]"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

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Davneet Singh

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.