Question

The coordinates of centre of mass of a system of three particles of masses 1μg , 2μg,3μg are (2,2,2) where should a fourth particle of mass 4 mg be positioned so that the centre of mass of the fourth particle system is at the origin of the 3-dimensional rectangular co-ordinate system?

Answer 1

we can change this problem like this:
(1+2+3)mg=6mg mass is at 2,2,2,
where to put 4mg mass to have COM at 0,0,0.
so 0=(6×2+4×x)/10
×=-3
similarly
y=-3 and
z=-3
so 4g mass is to b put at(-3,-3,-3)