Ex 10.4, 5 - Find if (2i + 6j + 27k) x (i + j + k) = 0 - Ex 10.4

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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﷯﷮ 2﷮1﷯﷮ 6﷮𝜆﷯﷮ 27﷮μ﷯﷯﷯ = 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 = 𝟐𝟕﷮𝟐﷯

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