The position vector of three particles of masses `m_1=1kg`.
`m_2=2kg` and `m_3=3kg` are `r_1=(hati+4hatj+hatk)m`, `r_2=(hati+hatj+hatk)m` and `r_3=(2hatj-hatj-2hatk)m` respectivley. Find the position vector of their centre of mass.

Explanation

The position vector of COM of the three particles will be given by
`vecr_(COM)=(m_(1)vecr_(1)+m_(2)vecr_(2)+m_(3)vecr_(3))/(m_(1)+m_(2)+m_(3))`
Substituting the values, we get
`vecr_(COM)=((1)(hati+4hatj+hatk)+(2)(hati+hatj+hatk)+(3)(2hati-hatj-2hatk))/(1+2+3)`
`=(1)/(2)(3hati+hatj-hatk)m`