Position vector of two particles of masses 200 g and 400 g at a given time are `3hati+hatj+9hatk ` m and `-2hati+6hatj-hatk`, respectively. Find the instantaneous position of the centre of mass of the system.

Explanation

To find the instantaneous position of the center of mass of the system consisting of two particles, we can follow these steps:

### Step 1: Identify the given data
- Mass of the first particle, \( m_1 = 200 \, \text{g} = 0.2 \, \text{kg} \)
- Mass of the second particle, \( m_2 = 400 \, \text{g} = 0.4 \, \text{kg} \)
- Position vector of the first particle, \( \mathbf{r}_1 = 3\hat{i} + \hat{j} + 9\hat{k} \, \text{m} \)
- Position vector of the second particle, \( \mathbf{r}_2 = -2\hat{i} + 6\hat{j} - \hat{k} \, \text{m} \)

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