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