向量a=(2,1)围绕原点按逆时针方向旋转π/4
设向量b=(x,y),y>0
则|a|=|b|=√5 ,∴x²+y²=5 ①
=π/4
∴cosπ/4=a●b/(|a||b|)=(2x+y)/5=√2/2
∴2x+y=5√2/2 ②
①②:x²+(5√2/2-2x)²=5
x²-2√2x+3/2=0
x=3√2/2,或 x=√2/2
x=3√2/2 y=-√2/2
或 x=√2/2,y=3√2/2
∴b=(√2/2,3√2/2)