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近日,笔者看到2016年1月北京市朝阳区高三第一学期期末试题第14题:已知点O在△ABC的内部,且有x((OA)|→)+y((OB)|→)+z((OC)|→)=(0|→),记△AOB,△BOC,△AOC的面积分别为S_(△AOB),S_(△BOC),S_(△AOC).若x=y=z=1,则S_(△AOB):S_(△BOC):S_(△AOC)=______;若x=2,y=3,z=4,则S_(△AOB):S_(△BOC):S_(△AOC)=______.分析第一问中点O为△ABC的重心,所以S_(△AOB):S_(△BOC):S_(△AOC)=1:1:1.第二问中由于系
Recently, I saw in January 2016, Chaoyang District, Beijing, the first semester of the third semester of the final question 14: Known point O △ ABC internal, and x ((OA) |) + y ((OB) →) + z ((OC) | →) = (0 | →), and the areas of △ AOB, △ BOC and △ AOC are S △ AOB, S △ BOC and S △ AOC, respectively. S_ (AOB): S_ (AOB): S_ (AOC) = ______ if x = 2, y = 3, z = 4 if x = y = z = (△ BOC): S_ (AOC) = ______. Analysis of the first question center O is the center of gravity of ABC, so S_ (AOB): S_ (BOC): S_ (AOC) = 1: 1: 1 The second question due to the Department