The position vectors of three particles of mass `m_(1) = 1kg, m_(2) = 2kg and m_(3) = 3kg` are `r_(1) = ((hat(i) + 4hat(j) +hat(k))`m, `r_(2) = ((hat(i)+(hat(j)+hat(k))`m and `r_(3) = (2hat(i) - (hat(j) -(hat(2k))`m, respectively. Find the position vector of their center of mass.

Explanation

To find the position vector of the center of mass of three particles with given masses and position vectors, we can follow these steps:

### Step 1: Identify the given data
We have three particles with the following properties:
- Masses:
- \( m_1 = 1 \, \text{kg} \)
- \( m_2 = 2 \, \text{kg} \)
- \( m_3 = 3 \, \text{kg} \)
...