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If $D\:\:and\:\:E$ are mid points of the side $\overline {AB}\:\:and\:\:\overline {AC}$ of a $\Delta \:ABC$, then $\overrightarrow {BE}+\overrightarrow {DC}=?$

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Let the position vectors of the points $,B,C$ be $\overrightarrow b,\overrightarrow c$ respectively.
with $A$ as origin.
Since $D\:and\:E$ are mid points of $\overline {AB} \:\:and\:\:\overline {AC}$,
Position vectors of $D \:and\: E$ are respectively $\large\frac{\overrightarrow b}{2}\:$ and $\large\frac{\overrightarrow c}{2}$
$\overrightarrow {BE}+\overrightarrow {DC}=\big(\large\frac{\overrightarrow c}{2}$$-\overrightarrow b\big)+\big(\overrightarrow c-\large\frac{\overrightarrow b}{2}\big)$
$=\large\frac{3}{2}$$(\overrightarrow c-\overrightarrow b)=\large\frac{3}{2}$$\overrightarrow {BC}$
answered Dec 3, 2013 by rvidyagovindarajan_1

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