Question

已知向量m=(a,b)向量n⊥向量m,向量m的模=向量n的模,则n的坐标是?

Answer 1

let n(x,y)

n⊥m

m.n =0

(a,b)(x,y) =0

ax+by=0

y= -ax/b (1)

|m|=|n|

=>a^2+b^2 = x^2+y^2 (2)

Sub (1) into (2)

a^2+b^2 = x^2+a^2x^2/b^2

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

x^2 =b^2

x= b or -b

x=b ,y = -a

x=-b, y=a

n = (b,-a) or (-b,a)