Question

If G is. Centroid of triangle ABC and O is any point then OA+Ob+OC=?

Answer 1

Answer:

3 OG

Step-by-step explanation:

The centroid is the centre of mass when equal masses are placed at each vertex.  So G is essentially the "arithmetic mean" of the vertices.  As OA, OB and OC are the position vectors of the vertices, and OG is the position vector of G, this means

      OG = ( OA + OB + OC ) / 3

=>   OA + OB + OC = 3 OG

Incidentally, if you put different masses at each vertex, the centre of mass is the "weighted arithmetic mean" of the vertices, and it will, of course, be a different point.  For instance, if the masses at A, B, C are proportional to the opposite sides BC, CA, AB, respectively, then the centre of mass is the incentre of the triangle.

Answer 2

Answer:

answer Is 3OG

Step-by-step explanation:

Let O be the origin OA,OB,OC be the position vectors of triangle ABC .

Let G be the centroid of the triangle ABC and OG be the position vector of it.

we know that mean of the points A,B,C is centroid(G)

=>(OA+OB+OC)/3    =    OG

=>OA+OB+OC          =   3OG

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