If the vectors $bold a bold space bold equals bold space bold i with bold hat on top bold space bold minus bold j with bold hat on top bold space bold plus bold 2 bold k with bold hat on top bold comma bold space bold b bold space bold equals bold 2 bold i with bold hat on top bold space bold plus bold 4 bold j with bold hat on top bold space bold plus bold k with bold hat on top bold space bold and bold space bold c bold space bold equals bold space bold lambda bold i with bold hat on top bold space bold plus bold j with bold hat on top bold space bold plus bold mu bold k with bold hat on top$ are mutually orthogonal, then (λ,μ) is equal to

(-3,2)

(2,-3)

(-2,3)

(3,-2)

Solution

(-3,2)

since, the given vectors mutually orthogonal, therefore
a.b = 2-4+2 = 0
a.c = λ-1 + 2μ = 0 ....(i)
b.c = 2λ + 4 +μ = 0 ... (ii)
On solving Eqs. (i) and (ii), we get
μ = 2 and λ = - 3
Hence, (λ,μ) = (-3,2)

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