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Pe o dreapta d se iau punctele M,N,P,Q in aceasta ordine. Sa se arate ca :
a) MP+NQ=MQ+NP
b) MP X NQ=MQ X NP + MN X PQ


Răspuns :

a)
NQ-NP=PQ    
MQ-MP=PQ   
Le egalam => NQ-NP=MQ-MP =>
NQ+MP=MQ+NP
b)
MP*(NP+PQ)=MP*NP + MP*PQ
MP*PQ=(MN+NP)*PQ=MN*PQ+NP*PQ
MP*NP=(MQ-PQ)*NP=MQ*NP-PQ*NP
Inlocuim in relatie de unde =>
MP*(NP+PQ)=MN*PQ+NP*PQ+MQ*NP-PQ*NP <=>
MP*(NP+PQ)=MN*PQ+MQ*NP