Ai giải giúp em với. Cho hình bình hành ABCD tâm O. Gọi G là trọng tâm tam giác ABC. Chứng minh: a) vectơ AB + vectơ AD = 2AO b) vectơ AB + vectơ AC + vectơ AD = 2AC c) vectơ AB + vectơ OD - 1/2 vectơ AC = vectơ 0 d) vectơ GA + vectơ GC = 1/3 vectơ BD

a.

`\vec{AB}+\vec{AD}`

`=\vec{AO}+\vec{OB}+\vec{AO}+\vec{OD}`

`=2\vec{AO}+(\vec{OB}+\vec{OD})`

`=2\vec{AO}+\vec{0}`

`=2\vec{AO}` (đpcm)

b.

`\vec{AB}+\vec{AC}+\vec{AD}`

`=\vec{AC}+\vec{AC}+\vec{AC}+(\vec{CB}+\vec{CD})`

`=3\vec{AC}+\vec{CD}`

`=3\vec{AC}-\vec{AC}`

`=2\vec{AC}` (đpcm)

c.

`\vec{AB}+\vec{OD}-1/2\vec{AC}`

`=\vec{AB}+\vec{OD}-1/2\vec{AB}-1/2\vec{AD}`

`=1/2\vec{AB}+\vec{OD}-1/2\vec{AD}`

`=1/2\vec{AD}+1/2\vec{DB}+\vec{OD}-1/2\vec{AD}`

`=1/2\vec{DB}+\vec{OD}`

`=\vec{DO}+\vec{OD}`

`=\vec{DD}`

`=\vec{0}` (đpcm)

d.

`\vec{GA}+\vec{GC}`

`=\vec{BG}`

`=2/3\vec{BO}`

`=2/3(1/2\vec{BD})`

`=1/3\vec{BD}` (đpcm)

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