OA 、OC、OD、OE等都表示向量,t表示倍数

OA 、OC、OD、OE等都表示向量,t表示倍数
已知3OA=OC,2OB=OD,OE=t （OA+OB）,则实数t为何值时,C、D、E 三点在同一条直线上?
因为OA=1/3OC,OB=1/2OD,所以OE=t/3 OC+t/2 OD,当且仅当t/3+t/2=1时
C、D、E三点共线.故t=6/5
,我不明白的就是为什么要t/3+t/2=1,

3OA=OC,2OB=OD,OE=t (OA+OB)
OA=(1/3)OC,OB=(1/2)OD
OE=t/3OC+ t/2OD
if E is on CD,then
let |CE|/|EC| = m:n
=> OE = (nCE +mEC)/(m+n)
Now
OE=t/3OC+ t/2OD
m+n = 1
n+m = (t/3) + (t/2) = 1