If G is the centroid of triangle ABC ,then the value GA + GB + GC = ?

Please help soon .

thank you .

Question

If G is the centroid of triangle ABC ,then the value GA + GB +
GC = ?
Please help soon
thank you

Priyanka Kedia · Accepted Answer

Let the position vectors of vertices A,B,C are a,b,c respectively
Let G→ be the centroid of triangle ABC So,p v of
G→=13OA→+OB→+OC→=13a+b+cThus,GA→=p v
of A→-p v of G→=a-13a+b+cGB→=p v of B→-p v
of G→=b-13a+b+cGC→=p v of C→-p v of
G→=c-13a+b+cOn
Adding,GA→+GB→+GC→=a-13a+b+c+b-13a+b+c+c-13a+b+c=0⇒GA→+GB→+GC→=0Hence
Proved

If G is the centroid of triangle ABC ,then the value GA + GB + GC = ? Please help soon . thank you .

If G is the centroid of triangle ABC ,then the value GA + GB + GC = ?

Please help soon .

thank you .