如图三角形ABC中,E,F分别是AB,AC的中点,G是EF的三等分点,设向量AB=a,向量AC=b,试用向量a,b表示向

∵ DE = DA + AE
∴ 本题就要找出DA和AE,用AB = a, AC = b来表达
∵ E为AB中点
∴ AE = 1/2 AB = 1/2 a
同理,AF = 1/2 AC = 1/2 b
∴ EF = EA + AF = AF - AE = 1/2 (a-b)
∵ G是EF的三等分点
∴ EG = 1/3 EF = 1/6 (a-b)
∴ AG = AE + EG = 1/2 a + 1/6(a-b) = 2/3 a - 1/6 b
∵ AD = 2AG
∴ AD = 4/3 a - 1/3 b
∴ DA = -AD = 1/3 b - 4/3 a
∴ DE = AD + AE = 1/3 b - 4/3 a + 1/2 a = 1/3 b - 5/6 a
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