Verified answer

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