设a(x,y) b(x',y')
则Ia+bI=√[(x+x')^2+(y+y')^2]
Ia-bI=√[(x-x')^2+(y-y')^2]
两式相等,并平方得 (x+x')^2+(y+y')^2=(x-x')^2+(y-y')^2
解得xx'+yy'=0
即a*b=0
所以向量a与向量b垂直