OABC is a tetrahedron. If D,E are the midpoints of OA and BC respectively, then $\bar{D E} =$

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$\frac{1}{2} (\bar{O A} + \bar{O B} + \bar{O C})$

$\frac{1}{2} (\bar{O A} + \bar{O B} - \bar{O C})$

$\frac{1}{2} (\bar{O A} - \bar{O B} + \bar{O C})$

$\frac{1}{2} (- \bar{O A} + \bar{O B} + \bar{O C})$

answer is D.

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Detailed Solution

$\bar{D E} = \bar{O E} - \bar{O D}$ $\bar{D}$ is midpoint of $\bar{O A}$
$= \frac{\bar{b} + \bar{c}}{2} - \frac{\bar{a}}{2}$ $\bar{E}$ is midpoint of BC

$= \frac{1}{2} (- \bar{O A} + \bar{O B} + \bar{O C})$

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