Find the position vector of a point R which divides the line joining the point `P(hati + 2hatj - hatk)` and `Q(-hati + hatj + hatk)` in the ratio `2 : 1`, (i) internally and (ii) externally.

Explanation

To find the position vector of a point \( R \) that divides the line segment joining points \( P \) and \( Q \) in the ratio \( 2:1 \), we will solve the problem in two parts: (i) internally and (ii) externally.

### Given:
- Point \( P = \hat{i} + 2\hat{j} - \hat{k} \)
- Point \( Q = -\hat{i} + \hat{j} + \hat{k} \)
- Ratio \( m:n = 2:1 \)

### (i) Finding the position vector of point \( R \) that divides \( PQ \) internally:
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