Direction Sense

Let's break the movement down:
- First, Deepa moves 75 meters towards the North.
- Then, she turns left and moves 80 meters. Since she was facing North, turning left makes her face West. So, she moves 80 meters towards the West.
- Finally, she turns right at a 45° angle. Since she was facing West, turning right means she will now face South-West (because the right turn from West at a 45° angle brings her diagonally to South-West).
Thus, the direction in which she is finally moving is South-West, corresponding to option (d).

Step 1: Represent the first displacement vector (north-east). Step 2: Represent the second displacement vector (north-west). Step 3: Find the resultant displacement vector . Step 4: Simplify the components.

Step 1: Visualize the movement.
The person starts at the origin, facing north:
1. He walks 8 km north.
2. Turns right (now facing east) and walks 4 km.
3. Turns right again (now facing south) and walks 6 km.
4. Finally, he turns left (now facing east) and walks 3 km.

Step 2: Calculate the final position.
- After walking north for 8 km, he is at (0, 8).
- After walking east for 4 km, he is at (4, 8).
- After walking south for 6 km, he is at (4, 2).
- After walking east for 3 km, he is at (7, 2).

Step 3: Calculate the distance from the starting point.
The distance between the starting point (0, 0) and the final position (7, 2) is given by the distance formula:

Step 4: Conclusion.
Thus, the person is 7.62 km from the starting point, and the correct answer is (c).

Let’s trace the man's path step-by-step.
Step 1: The man starts facing North and walks 10 meters.
He is now 10 meters North of his starting point.
Step 2: He then turns right.
Since he was facing North, turning right means now he faces East.
He walks 5 meters East.
Now, he is 10 meters North and 5 meters East of the starting point.
Step 3: He turns right again.
He was facing East, so now he faces South.
He walks 10 meters South.
So he moves from 10 meters North to back down to his starting latitude.
He is now 5 meters East of his original position, but facing South.
Hence, after all the movements, he is facing South.