Two bodies of mass 3g and 6g have position vectors `2hati+hatj+3hatk and hati+3hatj+2hatk` respectively.
Find the position vectors of center of mass.

Explanation

`"Mass M"_(1)=3g," "vec(r_(1))=2hati+hatj+3hatk`
`"Mass M"_(2)=6g," "vec(r_(2))=hati+3hatj+2hatk`
Position vector os centre of mass
`=(M_(1)r_(1)+M_(2)r_(2))/(M_(1)+M_(2))=(3(2hati+hatj+3hatk)+6(hati+3hatj+2hatk))/(3+6)`
`=(6hati+3hatj+9hatk+6i+18hatj+12hatk)/(9)`
`=(12hati+21hatj+21hatk)/(9)=(4)/(3)hati+(7)/(3)hatj+(7)/(3)hatk`
`therefore" Position vectors of centre of mass "=(4)/(3)hati+(7)/(3)hatj+(7)/(3)hatk.`