The positiion vectors of two point masses 10 kg and 5 kg are `(3hati+2hatj+4hatk)m and (3hati+6hatj+5hatk)m` respectively. Locate the position of center of mass.

Explanation

`m_(1)=10 kg`
`m_(2)= 5kg`
`vecr_(1)=(-3hati+2hatj+4hatk)m`
`vecr_(2)=(3hati+6hatj+5hatk)m`
`vecr=(m_(1) vecr_(1)+m_(2) vecr_(2))/(m_(1)+m_(2))`
`:. vecr=(10(-3hati+2hatj+4hatk)+5(3hati+6hatj+4hatk))/(10+5)`
`=(-30 hati+20 hatj+40 hatk+15hati+30 hatj+25 hatk)/(15)=(-15 hatk+50 hatj+65 hatk)/(15)`
`vecr=(-hati+(10)/(3) hatj+(13)/(3)hatk)`
The center of mass is located at position `vecr`