A man moves 3.5m towards east then he moves 2m in south then 4.5m towards east. Find its distance and displacement.

Distance is just the total amount he traveled (3.5 + 2 + 4.5 = 10m).

Displacement is the distance between his starting point and ending point (you may want to draw a picture for this). What you get is that he traveled a total of 8m east and 2m south.
Therefore, his total displacement is the length of the hypotenuse of a right triangle with sides 2 and 8 (= 8.25m).

In this case what will be the direction of displacement.

To find the distance and displacement, we need to analyze the man's movements in terms of vectors.

1. Draw a diagram: Start by drawing a diagram with a reference point (usually labeled "O" for the origin) and mark the man's movements. Let's assume East is to the right and North is up.

|
|
|_______O
| -->
| ---O
|

2. Analyze individual movements:
a) The man moves 3.5m towards the east. Draw an arrow from the origin (O) towards the right with a length of 3.5 units.

|
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------|_______O (3.5 units)
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|

b) Next, the man moves 2m towards the south. Draw an arrow from the end of the previous arrow (3.5 units to the right) downwards with a length of 2 units.

|
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------|_______O (3.5 units)
| |
| |

c) Finally, the man moves 4.5m towards the east. Draw an arrow from the end of the previous arrow (3.5 units to the right) to the right with a length of 4.5 units.

|
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------|_______O---- (3.5 units + 4.5 units)
| |
| |

3. Calculate the distance:
The distance is the total length covered by the man. We can find it by adding up the lengths of the individual movements.
Distance = 3.5m + 2m + 4.5m = 10m
Therefore, the total distance covered by the man is 10 meters.

4. Calculate the displacement:
Displacement is the shortest straight-line path from the initial point to the final point. It is the displacement vector that goes from the origin (O) to the final position of the man.
In this case, the man's final position is the end point of his last movement, which is 4.5 units to the right and 2 units downwards.

|
|
------|_______O---- (3.5 units + 4.5 units)
| |
| |

The displacement vector (represented by an arrow) goes from the origin (O) to this end point.

|
|
------|_______O---- (3.5 units + 4.5 units)
| |
| |
-->
-->

To find the displacement, we can use the Pythagorean theorem because it forms a right-angled triangle.
Displacement = √[(3.5)^2 + (2)^2] = √(12.25 + 4) = √16.25 ≈ 4.03m (rounded to two decimal places)
Therefore, the displacement of the man is approximately 4.03 meters.

In summary:
- The man covers a total distance of 10 meters.
- The man's displacement is approximately 4.03 meters.