向量|a|＝5,向量b=(2,-1),且a⊥b,求a坐标,

Question

向量|a|＝5,向量b=(2,-1),且a⊥b,求a坐标,

Answer 1

let a(x,y)
a.b=0
2x-y=0
y=2x (1)
|a|=5
x^2+y^2 =25
x^2+4x^2 =25
x=√5 or -√5
when x=√5 ,y = 2√5
when x=-√5,y =-2√5
a=(√5,2√5) or (-√5,-2√5)