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Study Stuff for MCA Examinations - NIMCET
Study Stuff for MCA Examinations - NIMCET
Previous Year Question (PYQs)
If the unit vectors $\vec a$ and $\vec b$ are inclined at an angle $2\theta$ such that
$|\vec a - \vec b| < 1$ and $0 \le \theta \le \pi$, then $\theta$ lies in the interval
Solution
$|\vec a - \vec b| = \sqrt{2-2\cos 2\theta}$
Given:
$\sqrt{2-2\cos 2\theta} < 1$
Squaring:
$2-2\cos 2\theta < 1$
$\cos 2\theta > \dfrac{1}{2}$
So,
$0 \le 2\theta < \dfrac{\pi}{3}$
$\Rightarrow 0 \le \theta < \dfrac{\pi}{6}$
From given options, valid interval is included in
$\left[0,\dfrac{\pi}{2}\right]$
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