Question

已知向量a=（-2,3），向量a平行于b，向量b的起点为A（1,2），终点B在坐标轴上，则点B的坐标为？

Answer 1

let 终点B =(x,y)
a //b
b = k(-2,3) ( k is a constant )
(x,y) -(1,2) = b = k(-2,3)
(x-1, y-2) =(-2k,3k)
=> x-1 = -2k and y-2 =3k
=> x= -2k+1 and y= 3k+2

B在坐标轴上 => x= 0 or y=0
case 1: x=0
k= 1/2, y=7/2
B(0,7/2)
case 2: y=0
k= -2/3 , x=7/3
B=(7/3,0)
ie
终点B= (0,7/2) or (7/3,0)