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Question

Find λ and μ if (2^i+6^j+27^k)×(^i+λ^j+μ^k)=0

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Solution

(2^i+6^j+27^k)×(^i+λ^j+μ^k)=0

∣ ∣ ∣^i^j^k26271λμ∣ ∣ ∣=0^i+0^j+0^k

^i(6μ27λ)^j(2μ27)+^k(2λ6)=0^i+0^j+0^k

On comparing the corresponding components, we have:

6μ27λ=0

2μ27=0

2λ6=0

Now,
2λ6=0λ=3

2μ27=0μ=272

Hence, λ=3 and μ=272.

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