xa+yb=x(3,4)+y(4,3)=(3x+4y,4x+3y)
∵向量a与向量(xa+yb)垂直
∴3(3x+4y)+4(4x+3y)=0
化简,得 25x+24y=0………………………………(1)
∵|xa+yb|=1
∴(3x+4y)^2+(4x+3y)^2=1
化简,得 25x^2 +48xy+25y^2=1…………………(2)
联立(1)(2)解得:
x=24/35,y=-5/7 或x=-24/35,y=5/7
∴所求x=24/35,y=-5/7 或x=-24/35,y=5/7
xa+yb=x(3,4)+y(4,3)=(3x+4y,4x+3y)
∵向量a与向量(xa+yb)垂直
∴3(3x+4y)+4(4x+3y)=0
化简,得 25x+24y=0………………………………(1)
∵|xa+yb|=1
∴(3x+4y)^2+(4x+3y)^2=1
化简,得 25x^2 +48xy+25y^2=1…………………(2)
联立(1)(2)解得:
x=24/35,y=-5/7 或x=-24/35,y=5/7
∴所求x=24/35,y=-5/7 或x=-24/35,y=5/7