2) démontrer que le vect IJ et le vect BC sont colinéaires
en utilisant la relation de Chasles
vect IA + vect AJ = vect IJ
nous savons que vect AI = 1/3 vect AB
vect CJ = 2/3 vect CA
vect IA = - vect AI =
vect AC = vect AJ + vect JC ⇒vect AJ = vect AC - vect JC = vect AC + vect CJ
vect AJ = vect AC + vect CJ = vect AC + 2/3 vect CA = vect AC - 2/3 vect AC = 1/3 vect AC
vect IA + vect AJ = vect IJ
vect IJ = - vect AI + 1/3 vect AC = - 1/3 vect AB + 1/3 AC = 1/3 vect BA + 1/3 vect AC = 1/3( vect BA + vect AC) = 1/3 vect BC
vect IJ = 1/3 vect BC
Donc IJ et BC sont colinéaires
vous faite le reste
