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Home  >>  CBSE XII  >>  Math  >>  Vector Algebra
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If $\mid\overrightarrow a\mid=10,\mid\overrightarrow b\mid=2$ and $\overrightarrow a.\overrightarrow b=12$,then value of $\mid\overrightarrow a\times\overrightarrow b\mid$ is

\[(A)\;5\quad(B)\;10\quad(C)\;14\quad(D)\;16\]
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1 Answer

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  • $\cos \theta =\large\frac{\overrightarrow a.\overrightarrow b}{|\overrightarrow a||\overrightarrow b|}$
Given $|\overrightarrow a|=10,|\overrightarrow b|=2$ and $\overrightarrow a.\overrightarrow b=12$
$\large\frac{\overrightarrow a.\overrightarrow b}{|\overrightarrow a||\overrightarrow b|}$$=\cos \theta$
On substituting the values we get,
$\cos \theta=\large\frac{12}{10 \times 2}=\frac{3}{5}$
If $\cos \theta=\large\frac{3}{5}$ then, $\sin \theta=\large\frac{4}{5}$
we know
$\sin \theta =\large\frac{|\overrightarrow a \times \overrightarrow b|}{|\overrightarrow a||\overrightarrow b|}$
On substituting the values we get,
$=>\large\frac{4}{5}=\frac{|\overrightarrow a \times \overrightarrow b|}{10 \times 2}$
$=|\overrightarrow a \times \overrightarrow b|=\large\frac{20 \times 4}{5}$$=16$
Hence $D$ is the correct option
answered Jun 3, 2013 by meena.p
 

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