Direction Sense

Compass directions: North (up), South (down), East (right), West (left) on a standard map. Diagonals: NE, NW, SE, SW.

Left and right relative to a direction:

• Facing North → right is East, left is West.
• Facing South → right is West, left is East.
• Facing East → right is South, left is North.
• Facing West → right is North, left is South.

A clean way to remember: clockwise = N→E→S→W→N. Right turn = clockwise; left turn = anti-clockwise.

Turn arithmetic:

• 90° right (clockwise) from N → E. From E → S. Etc.
• 180° from N → S (reverses).
• 270° clockwise = 90° anti-clockwise.

Sun shadow rule (often asked):

• In the morning, the sun is in the East, so shadows fall to the West.
• In the evening, sun is in the West, shadows fall to the East.
• At noon (in northern hemisphere), shadows fall to the North (the sun being south of you).

Diagonal distance (Pythagoras):
If you walk 3 km east and 4 km north, you are √(3² + 4²) = 5 km from the start, in a direction NE-ish.

General method:

1. Draw a coordinate-like sketch. Start at origin. Mark each move with arrow + distance.
2. After all moves, the displacement is from origin to final point.
3. For "distance from start", use Pythagoras.
4. For "direction from start", use which quadrant the endpoint is in.

Right-angle simplification: in most RRB problems, all turns are 90° multiples, so the path is rectilinear — straightforward addition/subtraction.

Example 1:
A man walks 4 km East, 3 km North, 4 km West, then 3 km North. How far is he from the start, and in which direction?
Method: East 4 then West 4 cancel. Net: 3 + 3 = 6 km North. Distance = 6 km North.

Example 2:
Raj starts facing East, turns right, walks 5 m. Turns left, walks 3 m. Turns left again, walks 5 m. Where is he relative to start?
Method: East → right = South. Walk 5 m south. Then left = East. Walk 3 m east. Then left = North. Walk 5 m north. Net displacement: 5 south + 5 north = 0 (north-south); 3 east. So he is 3 m east of start.

Example 3 — Pythagoras:
A boy walks 6 km North, then 8 km East. How far is he from start?
Method: √(6² + 8²) = √(36+64) = √100 = 10 km, in the NE direction.

Example 4 — Shadow problem:
At 7 am, a man sees his shadow falling to the right of his outstretched arm. Which way is he facing?
Method: At 7 am, sun is in the East, shadow points West. Shadow on the right → his right = West → he faces North.

Example 5 — Rotation chain:
Starting facing North, turn 90° right, then 180°, then 90° left. Direction now?
Method: N → E (right 90°) → W (180°) → S (left 90°). Final: South.

Quick reference — turn map:

Trap: when the question says "to his left/right", that's relative to the person's current facing, not the page/map orientation.