A(3,2,-1), B(4,1,1), C(6,2,5) are three points. If D, E, F are three points which divide B C , C A, A B respectively in the same ratio 2: 1 , then the centroid of D E F is

Step-by-step solution

Here, D= ( 2 6+4 1 3 , 2 2+1 1 3 , 2 5+1 1 3 )= ( 16 3 , 5 3 , 11 3 ) Similarly, E= ( 12 3 , 6 3 , 3 3 ) F= ( 11 3 , 4 3 , 1 3 ) Let centroid of D E F is O(x, y, z) . aligned & x= 16 3 + 12 3 + 11 3 3 = 13 3 & y= 5 3 + 6 3 + 4 3 3 = 5 3 and z= 11 3 +1+ 1 3 3 = 5 3 aligned Hence, coordinates are ( 13 3 , 5 3 , 5 3 ) .