14.Fx=70+40cosθ,Fy=40sinθ,
Fx^2+Fy^2=100^2=70^2+2*70*40*cosθ+40^2,
cosθ=0.625,
θ=arccos0.625=51.32°,
Fx=70+40cosθ=100cosβ,
cosβ=0.95,
β=18.19°.
2.若a⊥b,a.b=0,
|a+b|^2=(a+b).(a+b)=a.a+2a.b+b.b=|a|^2+|b|^2,
|a-b|^2=(a-b).(a-b)=a.a-2a.b+b.b=|a|^2+|b|^2,
|a+b|=|a-b|.
反之,若|a+b|=|a-b|,按上面过程反过来可以推出,a.b=0,a⊥b.
几何意义是：平行四边形中邻边相互垂直的充要条件是对角线相等.
3.若|a|=|b|,
c.d=(a+b).(a-b)=|a|^2-|b|^2=0,c⊥d.
若c⊥d,0=c.d=(a+b).(a-b)=|a|^2-|b|^2,|a|=|b|.
几何意义是：平行四边形中邻边相等的充要条件是对角线相互垂直.