Resultant Displacement

To determine the resultant displacement, we need to consider the individual displacements in each direction and combine them using vector addition.

Step 1: Eastward Displacement
The body travels a distance of 3 km towards the east. This can be represented as a displacement of +3 km in the x-axis.

Step 2: Northward Displacement
Next, the body travels 4 km towards the north. This can be represented as a displacement of +4 km in the y-axis.

Step 3: Eastward Displacement
Finally, the body travels 9 km towards the east. This can be represented as a displacement of +9 km in the x-axis.

Vector Addition
To find the resultant displacement, we need to add the individual displacements vectorially.

- We start by adding the eastward displacements: +3 km + 9 km = +12 km in the x-axis.
- Next, we add the northward displacement: +4 km in the y-axis.

Resultant Displacement
Using Pythagoras' theorem, we can find the magnitude of the resultant displacement:

resultant displacement = √((12 km)^2 + (4 km)^2)
resultant displacement = √(144 km^2 + 16 km^2)
resultant displacement = √160 km^2
resultant displacement ≈ 12.65 km

Direction of the Resultant Displacement
To find the direction of the resultant displacement, we can use trigonometry. The angle θ can be calculated as:

θ = tan⁻¹(4 km / 12 km)
θ ≈ 18.43°

Therefore, the resultant displacement is approximately 12.65 km with a direction of 18.43° north of east.

Summary
The body traveled 3 km east, 4 km north, and 9 km east. By adding the individual displacements vectorially, the resultant displacement is approximately 12.65 km with a direction of 18.43° north of east.