vectors( need answer asap)

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.

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  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>.

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