hello guys how are you i need your help plesase.
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 :
- 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).
- using the expression: vector(AG)+vector(BG)+vector(CG)=0, express the vector(AG) accrording to the vector(AB) and the vector(AC).
- show that we can write vector(AG)=Kvector(AJ) "AG=KAJ) " , for a certain k to be determined .
- deduce the the points A,G and J are aligned .
- in the same way it can be shown it can be shown that the ponints 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)
- 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.
