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Home  >>  CBSE XII  >>  Math  >>  Vector Algebra
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If $\mid\overrightarrow{a}\mid=4$ and $-3\leq\:\lambda\leq 2$,then the range of $\mid\lambda\overrightarrow{a}\mid$ is

\[(A)\;[0,8]\quad(B)\;[-12,8]\quad(C)\;[0,12]\quad(D)\;[8,12]\]
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  • $|\lambda\:\overrightarrow a|=|\lambda||\overrightarrow a|$
Given $|\overrightarrow a|=4 \: and\:-3\leq\lambda\leq\:2$
Since it is given $-3 \leq \lambda \leq 2$
This implies $0\leq|\lambda|\leq\:3$
Multiply this in equation by $ |\overrightarrow a|$ we get,
$=>0\leq|\lambda|\:|\overrightarrow a|\leq\:3|\overrightarrow a|$
But $|\lambda|\:|\overrightarrow a|=|\lambda\overrightarrow a|$ and $|\overrightarrow a|=4$
$=>0\leq\:|\lambda\overrightarrow a|\leq\:3\times4$
$=>0\leq\:|\lambda\overrightarrow a|\leq 12$
Hence the range of $\lambda \: is\: [0,12]$
Hence $C$ is the correct option
answered May 29, 2013 by meena.p
 

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