若向量a,b不共线，则向量p与a,b共面的充要条件是？

Question

如题所述

Answer 1

p,a,b三点共线,则存在唯一实数t,使得向量pa=tpb,
(oa-op)=t(ob-op),
(t-1)op=-oa+tob,
op=-1/(t-1)oa+t/(t-1)ob,
则a=-1/(t-1),b=
t/(t-1)
a+b=-1/(t-1)+
t/(t-1)=1.
则p,a,b三点共线的充要条件是a+b=1.