若平面向量a,b满足|a+b|=1,a+b平行于y轴,a=(2,-1),则b=_.

问题描述:

若平面向量

a
b
满足|
a
+
b
|=1,
a
+
b
平行于y轴,
a
=(2,-1),则
b
=______.

b
=(x,y)
a
+
b
平行于y轴,得出
a
+
b
=(x+2,y-1)=(0,y-1),解得x=-2
又∵|
a
+
b
|=1,∴(y-1)2=1
解得y=0,或y=2
b
=(-2,2)或(-2,0)
故答案为:(-2,2)(-2,0)