be ABC a triangle non flat,we define the isobarycentre of the triangle ABC the point G such that :
vector(AG)+vector(BG)+vector(CG)=0
the point G is the centre of gravity of the triangle ABC
QUESTIONS :
1.the respective points I,J and k are placed in the segments (AB),(BC) and (AC). express the vector AJ according to the vector(AB) and the vector(AC).
2.using the expression: vector(AG)+vector(BG)+vector(CG)=0, express the vector(AG) accrording to the vector(AB) and the vector(AC).
3.show that we can write vector(AG)=Kvector(AJ) "(AG=KAJ) " , for a certain k to be determined .
4.deduce the the points A,G and J are aligned .
5.in the same way it can be shown that the. points B,G and k are aligned , as are the points C,G and I , show that G is the the point of intersection of the lines (AJ),(BK) and (CI)
6.what is the position of the point G (the centre of gravity of the triangle ABC)
indication : if AB is a segment , the middle I of (AB) is the poin of intersection between the segment (AB) and its median.
Please I need help!!!.
