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Question

Find the values of λ for which the angle between the vectors the vectors a=2λ^2i+4λ^j+^k and b=^7i2^j+^λk is obtuse.

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Solution

cosθ=a.b|a.b|
=(2λ2^i+4λ^j+^k).(7^i2^j+λ^k)4λ4+16λ2+149+4+λ2
=14λ28λ+λ4λ4+16λ2+149+4+λ2
7(2λ2λ)+149+4+λ2
1cosθ0 for θ to be θb
cosθ0
λ(2λ1)0
λ[0,1/2] AS |cosθ|<1

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