(1)
AB=OB-OA=(2,1)-(1,-2)=(1,3)
AC=OC-OA=(3,2)-(1,-2)=(2,4)
AD=OD-OA
BD=OD-OB
CD=OD-OC
AD+BD+CD=3OD-OA-OB-OC
=(-6,9)-(1,-2)-(2,1)-(3,2)=(-12,8)
设AD+BD+CD=xAB+yAC
x(1,3)+y(2,4)=(x+2y,3x+4y)=(-12,8)
x+2y=-12
3x+4y=8
x=32,y=-22
所以:AD+BD+CD=32AB-22AC
(2)-1
AB=OB-OA
OB=AB+OA=(6,0)+(1,1)=(7,1)
BC=OC-OB
OC=BC+OB=AD+OB=(3,5)+(7,1)=(10,6)
点C的坐标(10,6)
(2)-2
MB=(1/2)AB=(3,0)
OM=(1/2)(OA+OB)=(1/2)((1,1)+(7,1))=(4,1)
|MP|/|PC|=|MB|/|DC|=|MB|/|AB|=1/2
所以：MC=3MP=3OP-3OM
MC=3OP-3OM
设OP=(x,y)
MC=MB+BC=MB+AD
所以：MB+AD=3OP-3OM
AD=-MB-3OM+3OP=-(3,0)-3(4,1)+3(x,y)=(3x-15,y-3)
而:|AD|=|AB|=6
所以:(3x-15)^2+(3y-3)^2=36
(x-5)^2+(y-1)^2=4