(向量)已知点A(1,-2),若向量AB与a=(2,3)同向,|AB|=2根号13,则B点坐标为?

B(x,y) AB{x-1,y+2} (x-1)/2=(y+2)/3 ,y+2=1.5(x-1) ,(1) |AB|^2=4*13=(x-1)^2+(y+2)^2 ,(2) (1)代入(2)：(x-1)^2*(1+1.5*1.5)=52 |x-1|=4 x= 5 ,y=4 or x=-3,y=-8 (舍)B(5,4)