Kartik starts from Point A and drives 11 km towards east. He then takes a right turn, drives 5 km, turns right and drives 14 km. He then takes a right turn and drives 11 km. He takes a final right turn, drives 3 km and stops at Point P.

How far (shortest distance) and towards which direction should he drive in order to reach Point A again?
(All turns are 90 degree turns only unless specified.)

The correct answer is 6 km to the south.

Let us trace Kartik's journey step-by-step from the starting point A, using a standard Cartesian coordinate system where Point A is the origin (0, 0). Let the positive x-axis represent East, negative x-axis represent West, positive y-axis represent North, and negative y-axis represent South.

Step 1: Kartik starts at Point A (0, 0) and drives 11 km towards the east.
His new position is at:
$(0+11,0)=(11,0)$

Step 2: He takes a right turn (which faces him South) and drives 5 km.
His new position is at:
$(11,0-5)=(11,-5)$

Step 3: He turns right again (which now faces him West) and drives 14 km.
His new position is at:
$(11-14,-5)=(-3,-5)$

Step 4: He takes another right turn (which faces him North) and drives 11 km.
His new position is at:
$(-3,-5+11)=(-3,6)$

Step 5: He takes a final right turn (which faces him East) and drives 3 km to stop at Point P.
His final position at Point P is at:
$(-3+3,6)=(0,6)$

Finding the return path to Point A:
Point A is located at the origin (0, 0), and Kartik's current position Point P is at (0, 6).
The difference in coordinates shows that Point P is exactly 6 km directly North of Point A.
Therefore, to reach Point A (0, 0) from Point P (0, 6), Kartik must drive straight down along the y-axis, which is a distance of 6 km towards the south.