Last updated at May 29, 2018 by Teachoo

Transcript

Ex 10.4, 5 Find λ and μ if (2 𝑖 + 6 𝑗 + 27 𝑘) × ( 𝑖 + 𝜆 j + μ 𝑘) = 0 Let 𝑎 = 2 𝑖 + 6 𝑗 + 27 𝑘 & 𝑏 = 1 𝑖 + 𝜆 j + μ 𝑘 Given, 𝑎 × 𝑏 = 0 𝑎 × 𝑏 = 𝑖 𝑗 𝑘 21 6𝜆 27μ = 𝑖 6×μ−(𝜆×27) − 𝑗 2×μ− 1×27 + 𝑘 2×𝜆−(1×6) = 𝑖 6μ−27𝜆 − 𝑗 2μ−27 + 𝑘 2𝜆−6 ∴ 𝑎 × 𝑏 = 6μ−27𝜆 𝑖 − (2μ−27) 𝑗 + (2𝜆 − 6) 𝑘 Also, 𝑎 × 𝑏 = 0 𝟔μ−𝟐𝟕𝜆 𝒊 − (𝟐μ−𝟐𝟕) 𝒋 + (2𝜆 − 6) 𝒌 = 0 𝒊 + 0 𝒋 + 0 𝒌 Comparing components Therefore, 𝜆 = 3 and μ = 𝟐𝟕𝟐

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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.