A particle undergoes three successive displacement in a plane as follows 4m southwest, 5m east, 6m in a direction 60 degree north of east (a) draw an apropraite vector diagram to represcent the displacement (b) detarmine the displacement that would be required to bring the particle back to the starting point

To solve this problem, we need to break down the given displacements into their respective x and y components. Then we can add up all the x and y components separately to find the final displacement.

(a) Drawing the vector diagram:
Let's label the three successive displacements as D1, D2, and D3.

1. D1: 4m southwest
- The southwest direction is a combination of south (downwards) and west (to the left).
- So, the x-component of D1 is -4cos(45°) = -2.83m (to the left)
- And the y-component of D1 is -4sin(45°) = -2.83m (downwards)

2. D2: 5m east
- The east direction is purely along the positive x-axis.
- So, the x-component of D2 is 5m (to the right)
- And the y-component of D2 is 0m (no vertical displacement)

3. D3: 6m at 60° north of east
- To determine the respective x and y components of D3, we need to resolve it into its x and y axes.
- The angle north of east is 90° - 60° = 30°.
- So, the x-component of D3 at 30° is 6cos(30°) = 5.2m (to the right)
- And the y-component of D3 at 30° is 6sin(30°) = 3m (upwards)

Now, we can draw the vector diagram:
```
-----> Δx 5.2 m
|
| D3
| ↑
| /
| /
| /
| /
| /
| / 6 m
∨/
Delta y

```
Note: The D2 displacement (5m east) is along the x-axis, so it will not have any impact on the vertical component (Δy) of the displacement.

(b) Determining the displacement to bring the particle back to the starting point:
To find the displacement required to bring the particle back to the starting point, we need to find the negative vector sum of all the given displacements.

Adding all the x-components:
Δx = -2.83m + 5m + 5.2m = 7.37m (to the right)

Adding all the y-components:
Δy = -2.83m + 0m + 3m = 0.17m (upwards)

Therefore, the displacement required to bring the particle back to the starting point is approximately 7.37m to the right and 0.17m upwards.

What is your question on this?

for a) arrange the vectors head to tail, then the resultant is from oritin to final head.

b. reverse a.

4.0 and 6.0 are both in x and y then5.0 is in the x axis