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Home  >>  JEEMAIN and NEET  >>  Mathematics  >>  Class12  >>  Vector Algebra

If $\theta$ is the angle between the vectors $\overrightarrow a$ and $\overrightarrow b$, and $ |\overrightarrow a.\overrightarrow b|=|\overrightarrow a\times\overrightarrow b|$, then $\theta$=?

$\begin{array}{1 1} 0 \\ \large\frac{\pi}{4} \\\large\frac{\pi}{3} \\ \large\frac{\pi}{3} \\ \large\frac{\pi}{2} \end{array} $

1 Answer

Toolbox:
  • $|\overrightarrow a.\overrightarrow b|=|\overrightarrow a||\overrightarrow b|cos\theta$
  • $|\overrightarrow a\times\overrightarrow b|=|\overrightarrow a||\overrightarrow b|sin\theta$
Given:$|\overrightarrow a.\overrightarrow b|=|\overrightarrow a\times \overrightarrow b|$
$\Rightarrow\:|\overrightarrow a||\overrightarrow b|cos\theta=|\overrightarrow a||\overrightarrow b|sin\theta$
$\Rightarrow\:cos\theta=sin\theta$
$\Rightarrow\:\theta=\large\frac{\pi}{4}$
answered Oct 28, 2013 by rvidyagovindarajan_1
 

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