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Question:

If the vectors a = i - j + 2k, b = 2i + 4j + k and c = λi + j + μk are mutually orthogonal, then (λ, μ) = ?

(2, -7)

(-7, 2)

(3, -6)

(-6, 3)

Solution:

Since a, b and c are mutually orthogonal then a.b = 0, b.c = 0, c.a = 0
Putting values
2λ + 4 + μ = 0
λ(-7) + 2μ = 0
Solving these equations, we get
λ = -7, μ = 2
Hence, option 'B' is correct.