Question

Fie ABCD un patrulater oarecare, E mijlocul segmentului AB, si M apartine BC si N apartine AD astfel incat $\frac{BM}{BC}$=$\frac{AN}{AD}$=$\alpha$.
Sa se exprime vectorii EM si EN in functie de $\alpha$ si vectorii EA, EC, ED.

Answer 1

Răspuns:

Faceti un desen conf. problemei.

Se vede ca EAvector+ADvector=ED vector Cum ANvector=kADvactor=k(EDvector-EAvector) si la fel ;EBvector+BCvector=ECvector Cum BMvector=k.BCvector=k(ECvector-

-EBvector )=k(ECvector+EA vector). Deci;EMvector=EBvector+BMvctor=k.ECvector+(k-1)EAvector

(EAvector=-EBvector)

si ENvector=EAvector+ANvector=kEDvector+(1-k)EAvector

am folosit k in loc de alfa