JEE MATHEMATICS MCQ: DOT PRODUCT OF VECTORS

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Analyzing +4 | -1

If the angle between the vectors

\mathbf{a}=\hat{\mathbf{i}}+(\cos x) \hat{\mathbf{j}}+\hat{\mathbf{k}}

and

\mathbf{b}=\left(\sin ^2 x-\sin x\right) \hat{\mathbf{i}}-(\cos x) \hat{\mathbf{j}}+(3-4 \sin x) \hat{\mathbf{k}}

is obtuse and

x \in\left(0, \frac{\pi}{2}\right)

, then the exhaustive set of values of '

x

' is equal to

View answer and explanation

Correct option: B

x \in\left(\frac{\pi}{6}, \frac{\pi}{2}\right)

Option B (

x \in (\frac{\pi}{6}, \frac{\pi}{2})

) is correct because the angle between the vectors is obtuse, implying their dot product is negative, which leads to the solution

x \in (\frac{\pi}{6}, \frac{\pi}{2})

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O A

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30^{\circ}

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