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# If $\overrightarrow a=2p\hat i+\hat j$ is rotated about an angle of $\theta$ in anti clock wise direction and becomes $(p+1)\hat i+\hat j$

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## 1 Answer

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Since the vector $\overrightarrow a$ is rotated, its magnitude is same
$\Rightarrow\:|2p\hat i+\hat j|=|(p+1)\hat i+\hat j|$
$\Rightarrow\:4p^2+1=p^2+2p+2$
$\Rightarrow\:3p^2-2p-1=0$
$\Rightarrow\:p=1$ or $p=\large\frac{1}{3}$
But if $p=1$ the vectors are same. $\therefore$ $p=\large\frac{1}{3}$
answered Dec 8, 2013

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