Prove OM = (OB + OC)/2 for any O,B,C,M

Prove that  OM = (OB + OC)/2 where OM,OB,OC are vectors. M is midpoint of BC. For any O.
Proof:
OM  = OB + BM = OB + (BC)/2
BC = OC - OB
=> OM = OB + OC/2 - OB/2 = (OB+OC)/2
H.P.

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