A man moves 20 m north, then 10m east and then `10sqrt2` m south-west. His displacement is 

Options

A. 20 m north
B. `10sqrt2` m north-west
C. 10 m north
D. `10sqrt2` m south-east

Explanation

To find the displacement of the man after he moves in the specified directions, we can break down the movements into vector components and then sum them up.

### Step-by-Step Solution:

1. **Initial Position**: Let's assume the man starts at the origin point O (0, 0).

2. **First Movement (20 m North)**:
- The man moves 20 m north. In vector form, this can be represented as:
\[ \vec{OA} = 20 \hat{j} \]
- The coordinates after this movement are (0, 20).

3. **Second Movement (10 m East)**:
- Next, he moves 10 m east. In vector form, this is:
\[ \vec{AB} = 10 \hat{i} \]
- The new coordinates after this movement are (10, 20).

4. **Third Movement (10√2 m Southwest)**:
- Moving southwest means moving at a 45-degree angle towards the south-west direction. The components of this movement can be calculated as follows:
- The southwest direction can be broken down into equal parts of south and west, which means:
\[ \vec{BC} = -10\sqrt{2} \cos(45^\circ) \hat{i} - 10\sqrt{2} \sin(45^\circ) \hat{j} \]
- Since \(\cos(45^\circ) = \sin(45^\circ) = \frac{1}{\sqrt{2}}\), we can simplify:
\[ \vec{BC} = -10\sqrt{2} \left(\frac{1}{\sqrt{2}}\right) \hat{i} - 10\sqrt{2} \left(\frac{1}{\sqrt{2}}\right) \hat{j} = -10 \hat{i} - 10 \hat{j} \]
- Now, the coordinates after this movement are:
- From (10, 20) moving to (10 - 10, 20 - 10) = (0, 10).

5. **Total Displacement**:
- The total displacement vector from the origin O (0, 0) to the final position C (0, 10) is:
\[ \vec{OC} = 0 \hat{i} + 10 \hat{j} \]
- This means the displacement is 10 m north.

### Final Answer:
The displacement of the man is **10 m North**.