已知点A(1,1)B(2,3)C(3,2)点p(x,y)在△ABC三边围成的区域(含边界)上
题目
已知点A(1,1)B(2,3)C(3,2)点p(x,y)在△ABC三边围成的区域(含边界)上
1)若向量PA+向量PB+向量PC=0,求向量|OP|
2)设向量OP=m向量AB+n向量AC,(m,n属于R),用x,y表示m-n,并求m-n的最大值
答案
(1)设:向量OP=(x,y)若:向量PA+向量PB+向量PC=(1-x,1-y)+(2-x,3-y)+(3-x,3-y)=(6-3x,6-3y)=0则:6-3x=0,6-3y=0,即:x=2,y=2,所以:向量OP=(2,2),︱OP︱=√(2^+2^)=2√2(2)向量OP(x,y)=m向量AB+n向量AC=m(2-1,3-...
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