If i is the position vector of the centroid G of triangle ABC and 2 i + j + k are respectively the position vectors of its vertices A and B , then AG ^2+ BG ^2+ CG ^2=

Step-by-step solution

Let vertex of c is (x i +y j +z k ) aligned & Centroid G=i+0 j +0 . k & = (2 i + j + k )+(2 i +4 j -4 k )+(x i +y j +z k ) 3 aligned aligned & 3=4+x x=-1 & or 0=5+y y=-5 & or 0=-3+z z=3, so, c(-1,-5,3) & Now, AG ^2+ BG ^2+ CG ^2 & = (1^2+1^2+1^2 )+ (1^2+4^2+4^2 )+ (2^2+5^2+3^2 ) & =3+33+38=74 aligned