If the angle between the vectors and is obtuse and

MATHEMATICS · Single correct · AP · AP Precalculus · Functions with Parameters, Vectors, and Matrices · Functions with Parameters, Vectors, and Matrices

Problem

If the angle between the vectors a=i^+(cos⁡x)j^+k^\mathbf{a} = \hat{i} + (\cos x)\hat{j} + \hat{k} and b=(sin⁡2x−sin⁡x)i^−(cos⁡x)j^+(3−4sin⁡x)k^\mathbf{b} = (\sin^2 x - \sin x)\hat{i} - (\cos x)\hat{j} + (3 - 4\sin x)\hat{k} is obtuse and x∈(0,π2)x \in \left(0, \frac{\pi}{2}\right) , then the exhaustive set of values of ' xx ' is equal to (1) x∈(0,π6)x \in \left(0, \frac{\pi}{6}\right) (2) x∈(π6,π2)x \in \left(\frac{\pi}{6}, \frac{\pi}{2}\right) (3) x∈(π6,π3)x \in \left(\frac{\pi}{6}, \frac{\pi}{3}\right) (4) x∈(π3,π2)x \in \left(\frac{\pi}{3}, \frac{\pi}{2}\right)

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