The centroid of the triangle OAB is denoted by G. If O is the origin and OA=4i + 3j ,OB=6i-j. Find OG in terms of the unit vectors, I and j.

Answer 1

The centroid of a triangle is located at 2/3 of the length of any median.
Median=(OA+OB)/2=<5,1>
2/3 from vertex (origin)=<10/3,2/3>.

Another way:
It turns out that the coordinates of the centroid of a triangle is the mean of the x and y coordinates of the vertices.
In this case, the coordinates are:
<0,0>
<4,3>
<6,-1>
The mean of x=10/3, mean of y=2/3
So G is at <10/3,2/3>.