The centre of mass of three particles of masses `1 kg, 2kg and 3 kg` lies at the point `(3m, 3m, 3m)` where should a fourth particles of mass `4 kg` be positioned so that centre of mass of the four particle system at `(1m, 1m, 1m)`?

Explanation

To find the position of the fourth particle such that the center of mass of the four-particle system is at the point (1m, 1m, 1m), we can follow these steps:

### Step 1: Understand the Center of Mass Formula
The center of mass (CM) of a system of particles is given by the formula:
\[ \vec{R}_{CM} = \frac{M_1 \vec{r}_1 + M_2 \vec{r}_2 + M_3 \vec{r}_3 + M_4 \vec{r}_4}{M_1 + M_2 + M_3 + M_4} \]
where \(M_i\) is the mass of the \(i^{th}\) particle and \(\vec{r}_i\) is its position vector.
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