If the origin is the centroid of a triangle ABC having vertices `A(a ,1,3),\ B(-2, b ,-5)a n d\ C(4,7, c)` , find the values of `a , b , cdot`

Explanation

Given; Triangle ABC having vertices` A (a, 1, 3), B (– 2, b, – 5) and C (4, 7, c)` and origin is the centriod.


For a triangle the coordinates of the centroid is given by the average of the coordinates of its vertices.


`=> (0,0,0)=((a+(-2)+4)/3, (1+b+7)/3, (3+(-5)+c)/3)`


`=> (a+2)/3=0`

then, `a=-2`
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