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Question:

Find λ and μ if (î + 3ĵ + 9k) × (3î − λĵ + μk) = 0

Solution:

Given (î + 3ĵ + 9k) × (3î − λĵ + μk) = 0
Now we should do cross product of two given vectors and equate it to zero
∣∣∣∣∣ijk1393−λμ∣∣∣∣∣=i(3μ+9λ)+j(27−μ)+k(−3λ−9)=0
Hence, 3μ+ 9λ=0
27−μ=0
−3λ−9=0
Solving above three equations, we get,
μ=27,
λ=−3