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Question
What are the values of x for which the angle between the vectors? `2x^2hati + 3xhatj + hatk` and `hati - 2hatj + x^2hatk` is obtuse?
Solution
Let `veca = 2x^2hati + 3xhatj + hatk` and `vecb = hati - 2hatj + x^2hatk`
∵ Angle between the vectors is obtuse
`\implies` cos θ < 0
`\implies (veca.vecb)/(|veca||vecb|) < 0`
`\implies veca . vecb < 0`
`\implies` 2x2 – 6x + x2 < 0
`\implies` 3x(x – 2) < 0
`\implies` 0 < x < 2
i.e. x ∈ (0, 2)
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