hey i think this is a 3d question

i have the soln in 3 d

let the vector OA=a and the vector OB=b and the vector OC=c.centroid of the triangle is given by OG=a+b+c/3

then (OA)²+(OB)²+(OC)²=a²+b²+c²

then GA²=((b+c-2a)/3)² ,GB²=((a+c-2b)/3)²,GC²=((b+a-2c)/3)²

then GA²+GB²+GC²+3OG²=9a²+9b²+9c²/9 this is equal to OA²+OB²+OC²