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Given the vectors a=î-ĵ+2k̂, b=2î+4ĵ+k̂, and c=λî+ĵ+μk̂, if all three are pairwise perpendicular, then the pair (λ,μ) is

1. (2, -3)
2. (-2, 3)
3. (3, -2)
4. (-3, 2)

Correct answer: (-3, 2)

Solution

The vectors are pairwise perpendicular if their dot products are zero. By calculating the dot products of ( ext{a} cdot c, b cdot c, a cdot b, and solving the resulting equations, we find that the values of ( ext{lambda} and ( ext{mu} that satisfy all conditions are (-3, 2).

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