O为△ABC内一点,记a=S△BCO/S△ABC,b=S△CAO/S△ABC,r=S△ABO/S△ABC求→→→aOA+bOB+rOC的值答案是0向量

Question

O为△ABC内一点,记a=S△BCO/S△ABC,b=S△CAO/S△ABC,r=S△ABO/S△ABC求
→ → →
aOA+bOB+rOC的值
答案是0向量

Answer 1

题目等价为-向量OC=a/rOA+b/rOB使用几何法作出OC'=-OC(反向延长),再作C‘P∥OA于P此时只需证明OP/OA=S△BCO/S△ABO C'P/OB=S△CAO/S△ABO即可,以OP/OA=S△BCO/S△ABO为例子S△BCO=S△BC’O=S△BPO∴S△BCO/S△ABO=...