向量AO=xAB+yAC=(1-2y)AB+yAC, 平方，AO^2=4(1-2y)^2+9y^2+2y(1-2y)AB·AC,① OB=AB-AO=2yAB-yAC, 平方，OB^2=16y^2+9y^2-4y^2*AB·AC,② OC=AC-AO=(2y-1)AB+(1-y)AC, OC^2=4(2y-1)^2+9(1-y)^2+2(2y-1)(1-y)AB·AC,③ 因O是△ABC的外心，故AO^2=OB^2=OC^2, ①-②，0=4（1-4y)+2yAB·AC,④ ①-③，0=-9（1-2y)+2(1-2y)AB·AC,⑤ ④+⑤/2，AB·AC=0.5+7y,⑥ 代入④，4-16y+y+14y^2=0,14y^2-15y+4=0,y1=4/7,y2=0.5. 代入⑥，AB·AC=4.5,cosBAC=0.75; AB·AC=4,cosBAC=2/3.
答：向量AO=xAB+yAC=(1-2y)AB+yAC, 平方，AO^2=4(1-2y)^2+9y^2+2y(1-2y)AB·AC,① OB=AB-AO=2yAB-...详情>>
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