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Home  >>  JEEMAIN and AIPMT  >>  Mathematics  >>  Class12  >>  Vector Algebra
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If $|\overrightarrow a|=|\overrightarrow b|=1$ and $|\overrightarrow a+\overrightarrow b|=\sqrt 3$ and $\overrightarrow c$ is such that $\overrightarrow c-\overrightarrow a-2\overrightarrow b=3(\overrightarrow a\times\overrightarrow b)$, then $\overrightarrow c.\overrightarrow b=?$

$\begin{array}{1 1} \frac{-1}{2} \\ \frac{1}{2} \\ \frac{3}{2} \\ \frac{5}{2}\end{array} $

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Given: $|\overrightarrow a+\overrightarrow b|=\sqrt 3$
$\Rightarrow\:|\overrightarrow a|^2+|\overrightarrow b|^2+2\overrightarrow a.\overrightarrow b=3$
$\Rightarrow\:1+1+2\overrightarrow a.\overrightarrow b=3$
$or\:\: \overrightarrow a.\overrightarrow b=\large\frac{1}{2}$
Also given : $\overrightarrow c-\overrightarrow a-2\overrightarrow b=3(\overrightarrow a\times\overrightarrow b)$
$\Rightarrow\:(\overrightarrow c-\overrightarrow a-2\overrightarrow b).\overrightarrow b=3(\overrightarrow a\times\overrightarrow b).\overrightarrow b$
$\Rightarrow\:\overrightarrow c.\overrightarrow b-\overrightarrow a.\overrightarrow b-2|\overrightarrow b|^2=0$
$\Rightarrow\:\overrightarrow c.\overrightarrow b-\large\frac{1}{2}$$-2=0$
or $\overrightarrow c.\overrightarrow b=\large\frac{5}{2}$
answered Nov 19, 2013 by rvidyagovindarajan_1

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