Find the position vector of a point R which divides the line joining `A(-2,1,3)` and `B(3,5,-2)` in the ratio `2 : 1` (i) internally (ii) externally.

Explanation

To find the position vector of a point \( R \) that divides the line segment joining points \( A(-2, 1, 3) \) and \( B(3, 5, -2) \) in the ratio \( 2:1 \), we will use the section formula. We will solve this problem in two parts: first for internal division and then for external division.

### Part (i): Internal Division

1. **Identify the coordinates of points A and B**:
- \( A = (-2, 1, 3) \)
- \( B = (3, 5, -2) \)

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