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L and M are two points with position vectors $2\overrightarrow{a}-\overrightarrow{b}$ and $\overrightarrow{a}+2\overrightarrow{b}$ respectively.Write the position vector of a point N which divides the line segment LM in the ratio 2 : 1 externally.

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Let $\overrightarrow{OL}=2\overrightarrow{a}-\overrightarrow{b}$
$\overrightarrow{OM}=\overrightarrow{a}+2\overrightarrow{b} \qquad ratio=2:1$
$=\large\frac{2\overrightarrow{a}+4\overrightarrow{b}-2 \overrightarrow{a}+ \overrightarrow{b}}{1}$
answered Mar 24, 2013 by meena.p

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