(1)设X(x,y),在OP上 利用向量OP‖向量OX,得x=2y
XA=(1-x),XB=(5-x,1-y)
XA·XB=(x-1)(x-5)+(y-1)(y-7)=5y^2-20y+12=5(y-2)^2-8
∴OX(4,2)时,XA·XB取最小值-8
(2)XA=(-3,5) XB=(1,-1)
cos∠AXB=(XA·XB)/(|XA|·|XB|)=-4√17/17
(1)设X(x,y),在OP上 利用向量OP‖向量OX,得x=2y
XA=(1-x),XB=(5-x,1-y)
XA·XB=(x-1)(x-5)+(y-1)(y-7)=5y^2-20y+12=5(y-2)^2-8
∴OX(4,2)时,XA·XB取最小值-8
(2)XA=(-3,5) XB=(1,-1)
cos∠AXB=(XA·XB)/(|XA|·|XB|)=-4√17/17