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Home  >>  JEEMAIN and AIPMT  >>  Mathematics  >>  Class12  >>  Vector Algebra
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If $\overrightarrow a\:\:and\:\:\overrightarrow b$ are unit vectors that are inclined at angle $2\theta$ where $0\leq \theta \leq \pi$ and $|\overrightarrow a-\overrightarrow b| < 1$ then $ \theta$ lies in the interval....

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Given: $|\overrightarrow a-\overrightarrow b|<1$
$\Rightarrow\: |\overrightarrow a-\overrightarrow b|^2<1$
$\Rightarrow\:|\overrightarrow a|^2+|\overrightarrow b|^2-2\overrightarrow a.\overrightarrow b<1$
$\Rightarrow\:1-2cos2\theta<0$
or $cos2\theta>\large\frac{1}{2}$
$\Rightarrow\:0\leq \theta <\large\frac{\pi}{6}$ or $\large\frac{5\pi}{6}$$<\theta\leq \pi$
$\therefore\:$ $\theta$ lies in the interval $[0,\large\frac{\pi}{6})$
answered Dec 8, 2013 by rvidyagovindarajan_1
 

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