Find the coordinates of the point which divides the line segment joining the points `( 2, 3, 5)`and `(1, 4, 6)`in the ratio
(i) `2 : 3`internally, (ii) `2 : 3`externally.

Explanation

To find the coordinates of the point that divides the line segment joining the points \( P(2, 3, 5) \) and \( Q(1, 4, 6) \) in the given ratios, we will use the section formula for both internal and external division.

### Part (i): Internal Division in the Ratio \( 2:3 \)

1. **Identify the points and the ratio**:
- Let \( P(2, 3, 5) \) be \( (x_1, y_1, z_1) \) and \( Q(1, 4, 6) \) be \( (x_2, y_2, z_2) \).
- The ratio \( m:n = 2:3 \).

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