The three particles of mass `m , 2m` and `3m` are located at `(1 , 2, 3) , ( 2, 3, 4)` and `(1, 1,1)`. Find the position vector of `c.m.`

Explanation

Position vector is given by `vec(r ) = xhat(i) + y hat(j) + z hat(k)`
`m_(1) = m , vec(r_(1)) = hat(i) + 2 hat(j) + 3 hat(k)`
`m_(2) = 2m , vec(r_(2)) = 2 hat(i) + 3hat(j) + 4 hat(k)`
`m_(3) = 3m , vec(r_(3)) = hat(i) + hat(j) + hat(k)`
`vec(R)_(c.m.) = (m_(1) vec(r_(1)) + m_(2) vec(r_(2)) + m_(3) vec(r_(3)))/(m_(1) + m_(2) + m_(3))`
`= (m(hat(i) + 2hat(j) + 3hat(k)) + 2m( 2hat(i) + 3 hat(j) + 4 hat(k))+3m(hat(i) + hat(j) + hat(k)))/(m + 2m + 3m)`
`( 8 hat(i) + 11 hat(j) + 14 hat(k))/(6)`