Question

设O为原点, =(3,1), =(-1,2), ⊥,∥,试求满足+=的的坐标.

Answer 1

解析:设=(x,y),

则=+=(x+3,y+1),

=-=(x+4,y-1).

由⊥,得-(x+3)+2(y+1)=0,

即x-2y+1=0.                                   ①

由∥,得3(y-1)-(x+4)=0,

即x-3y+7=0.                                   ②

由①②联立,解得x=11,y=6,

即坐标为(11,6).