Question
Center of mass of a system of three particles of masses 2kg, 4kg and 6kg is at P ↔ (-2,0,4). If 6kg mass is removed from system, the center of mass of system shifts to Q ↔ (1,2,4). Find the position co-ordinates of 6kg mass.
Solution
Consider, 
be the position vectors of masses 2 kg, 4 kg and 6 kg respectively. The position coordinates of the centre of mass of 2 kg, 4 kg and 6 kg is (-2, 0, 4).
Therefore position vector of the centre of mass of 2 kg, 4 kg and 6 kg is,
R1 = -2
+ 0 
+ 4 
Also, 
Therefore, 
Therefore, 
... (1)
The position coordinates of centre of mass of 2kg and 4kg is (1, 2, 4).
Therefore position vector of centre of mass of 2kg and 4 kg is, 
Also, 
From (2) from (1), we get
The position vector of 6kg mass is, 
Therefore, position coordinate of 6 kg is ( -5, -2, 4).
