If the origin is the centroid of a triangle ABC having vertices A (a, 1, 3), B (– 2, b, – 5) and C (4, 7, c), find the values of a, b, c.
Given: Vertices of triangle ABC are-
A(z,1,3), B(-2,b,-5) & C(4,7,c)
& centroid, G = (0,0,0)
Thus, G(0,0,0) = G(a-2+4/3, 1+b+7/3, 3-5+c/3)
Thus, a+2/3 = 0
a = -2
b+8/3 = 0
b = -8
c-2/3 = 0
c = 2