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Answer the following.
What are the values of x for which the angle between the vectors 2x²î + 3xĵ + k̂ and î - 2ĵ +…
What are the values of $x$ for which the angle between the vectors $2x^2\hat{i} + 3x\hat{j} + \hat{k}$ and $\hat{i} - 2\hat{j} + x^2\hat{k}$ is obtuse? (Application)
Answer
Answer
Official answer keyThe angle is obtuse when $\cos\theta < 0$, i.e. $\vec a\cdot\vec b < 0$: $2x^2 - 6x + x^2 < 0 \Rightarrow 3x(x-2) < 0 \Rightarrow 0 < x < 2$.
Ans: $x \in (0, 2)$