Question

设平面内有四个向量a,b,x,y且满足a=y-x,b=2x-y,a垂直b,|a|=|b|=1,求|x|+|y|的值

Answer 1

(1)

a+b=(y-x)+(2x-y)=x

2a+b=(2y-2x)+(2x-y)=y.

(2) cost=x.y/(|x||y|)

由a⊥b知a.b=0.

x.y=(a+b).(2a+b) = a.2a+b.b=2+1=3

x.x=(a+b).(a+b)=a.a+b.b=2

y.y=(2a+b).(2a+b)=4a.a+b.b=5

所以cost=3/(sqrt(2)*sqrt(5))=3/sqrt(10)