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If $a, b, c$ are the position vectors of the vertices A, B, C of the triangle ABC, then the equation of the median from A to BC is

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$r = a + t (b + c)$

$r = a + t [\frac{1}{2} (b + c) - a]$

$r = a + t (b) + c$

$r = - a + t (b) + c$

answer is B.

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Detailed Solution

$OA = a OB = b OC = c BC midpoint = \frac{b + c}{2} eq of line passing through OA and midpoint of BC is r = a + t (\frac{b + c}{2} - a)$

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