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Home  >>  CBSE XII  >>  Math  >>  Vector Algebra
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If the sum of two unit vector is a unit vector, then what is the angle between them?

$\begin{array}{1 1} \large\frac{\pi }{6} \\\large\frac{\pi }{3} \\ \large\frac{ 2 \pi }{3}\\ \large\frac{\pi }{8} \end{array} $

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1 Answer

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Toolbox:
  • $|\overrightarrow a+\overrightarrow b|^2=|\overrightarrow a|^2+|\overrightarrow b|^2+2\overrightarrow a.\overrightarrow b$
  • $\overrightarrow a.\overrightarrow b=|\overrightarrow a|\:|\overrightarrow b|\:cos\theta$
Given: $\overrightarrow a,\overrightarrow b\:\:and\:\:\overrightarrow a+\overrightarrow b$ are unit vectors.
$\Rightarrow\:|\overrightarrow a|=|\overrightarrow b|=|\overrightarrow a+\overrightarrow b|=1$
We know that $|\overrightarrow a+\overrightarrow b|^2=|\overrightarrow a|^2+|\overrightarrow b|^2+2\overrightarrow a.\overrightarrow b$
$\Rightarrow\:|\overrightarrow a+\overrightarrow b|^2=|\overrightarrow a|^2+|\overrightarrow b|^2+2|\overrightarrow a|\:|\overrightarrow b|\:cos\theta$
$\Rightarrow\:1=1+1+2cos\theta=2+2cos\theta$
$\Rightarrow\:cos\theta=-\frac{1}{2}$
$\therefore\:\theta=\large\frac{2\pi}{3}$
answered Feb 3, 2014 by rvidyagovindarajan_1
 

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