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DABCD₁A₁B₁C₁  куб

DA  = a  ; DC = b  ;   DD₁ = c   и пусть |a| = |b|  = |c| = e (длина ребра куба)

AE/EB =5 /3  ;  CF /FC₁  = 1 /3

- - - - - - -

DE - ? EF - ?

* * * AB = DC = b ;  BC = AD =  - DA = - a  * * *

DE =DA + AE =DA + (5/8)*AB =DA + (5/8)*DC =  1*a +(5/8)*b + 0*c

DE { e ; (5/8)е ; 0 }

* * *  AE/EB  = 5 /3 ⇒  AE/AB = 5/8⇔ AE =(5/8)*AB=5/8*(DC)  * * *

- - - - - - -

EF = EC +CF = (EB + BC) + (1/4)*CC₁ =(3/8)*AB +BC +(1/4)*CC₁ =

(3/8)*DC + AD + (1/4)*DD₁ =(3/8)*DC - DA + (1/4)*DD₁ = - a + (3/8)*b+(1/4)*c =

- 1*a + 0,375*b+ 0,25*c

EF { - e ;0,375 е ; 0,25e}

* * * CF/FC₁  = 1 /3  ⇒ CF = (1/4)CC₁ = (1/4)*DD₁  * * *

Ответ:

DE = 1*a +(5/8)*b + 0*c ;

EF = -1*a + 0,375*b+ 0,25*c .

EB /AE =3 /5 ⇔EB /AE +1  =3 /5 + 1 ⇔(AE +EB) /AE =(5+3) /5⇔AB /AE=8/5