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Home  >>  JEEMAIN and AIPMT  >>  Mathematics  >>  Class12  >>  Vector Algebra
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$|\overrightarrow a|=3,\:|\overrightarrow b|=4,\:|\overrightarrow a+\overrightarrow b|=5,$ then $|\overrightarrow a-\overrightarrow b|=?$

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  • $|\overrightarrow a+\overrightarrow b|^2=|\overrightarrow a|^2+|\overrightarrow b|^2+2(|\overrightarrow a||\overrightarrow b|cos\theta)$
  • $|\overrightarrow a-\overrightarrow b|^2=|\overrightarrow a|^2+|\overrightarrow b|^2-2(|\overrightarrow a||\overrightarrow b|cos\theta)$
$|\overrightarrow a+\overrightarrow b|^2=|\overrightarrow a|^2+|\overrightarrow b|^2+2(|\overrightarrow a||\overrightarrow b|cos\theta)$
$\Rightarrow\:25=9+16+2\times3 \times 4cos\theta$
$\Rightarrow\:25=25+24cos\theta$
$\Rightarrow cos\theta=0$
$\therefore\:|\overrightarrow a-\overrightarrow b|^2=|\overrightarrow a|^2+|\overrightarrow b|^2-2(|\overrightarrow a||\overrightarrow b|cos\theta)$
$=9+16+0=25$ $\Rightarrow |\overrightarrow a-\overrightarrow b|=5$
answered Nov 6, 2013 by rvidyagovindarajan_1
 

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