Question

已知a=(3,4),b=(4,3),c=xa+yb,且a⊥c,|c|=1,求x和y的值?（向量）

Answer 1

c=(3x+4y,4x+3y)

3(3x+4y)+4(4x+3y)=0

(3x+4y)^2+(4x+3y)^2=1

(3x+4y)=-4(4x+3y)/3

16(4x+3y)^2+9(4x+3y)^2=9

(4x+3y)^2=9/25

4x+3y=3/5 or -3/5

4x+3y=3/5,(3x+4y)=-4/5,3x+3y=-3/35,x=24/35,y=-25/35

4x+3y=-3/5,(3x+4y)=4/5,3x+3y=3/35,x=-24/35,y=25/35