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Find λ and μ if (i+3j+9k)×(3i−λj+μk)= - Mathematics

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Find λ and μ if

`(hati+3hatj+9k)xx(3hati-lambdahatj+muk)=0`

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Solution

`(hati+3hatj+9k)xx(3hati-lambdahatj+muk)=0`

`|(hati,hatj,hatk),(1,3,9),(3,-lambda,mu)|=vec0`

`hati(3mu+9lambda)-hatj(mu-27)+hatk(-lambda-9)=vec0`

3μ + 9λ = 0 ...(1)

27 - μ = 0 ...(2)

-λ-9 = 0 ...(3)

by eqn (2) & (3)  μ = 27 and  λ = -9

So  μ = 27, λ = -9

Concept: Determinant of a Square Matrix
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