The three initial and final positions of a man on the x-axis are given as
(i) (-3 m, 7 m) (ii) (7 m, -3 m)
(iii) (-7 m, 3 m)

Options

A. (i)
B. (ii)
C. (iii)
D. i) and iii)

Explanation

To solve the problem of finding the displacement for the given initial and final positions on the x-axis, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Displacement**: Displacement is defined as the change in position of an object. It can be calculated using the formula:
\[ \text{Displacement} = \text{Final Position} - \text{Initial Position} \]

2. **Calculating Displacement for Each Case**:

**Case (i)**: Initial position = -3 m, Final position = 7 m
\[ \text{Displacement} = 7 \, \text{m} - (-3 \, \text{m}) = 7 \, \text{m} + 3 \, \text{m} = 10 \, \text{m} \]

**Case (ii)**: Initial position = 7 m, Final position = -3 m
\[ \text{Displacement} = -3 \, \text{m} - 7 \, \text{m} = -10 \, \text{m} \]

**Case (iii)**: Initial position = -7 m, Final position = 3 m
\[ \text{Displacement} = 3 \, \text{m} - (-7 \, \text{m}) = 3 \, \text{m} + 7 \, \text{m} = 10 \, \text{m} \]

3. **Summary of Results**:
- For Case (i): Displacement = 10 m
- For Case (ii): Displacement = -10 m
- For Case (iii): Displacement = 10 m