Setting up a coordinate system with P at the origin and the initial direction along the positive x-axis.
P is at (0,0)
Alok walks 6 km to point Q:
Q is at (6,0)
At Q, Alok turns right and walks 12 km to point R.
Turning right from the positive x-direction means moving in the negative y-direction.
R is at (6,−12)
At R, Alok turns right again and walks 11 km to point S.
Turning right from the negative y-direction means moving in the negative x-direction.
S is at (6−11,−12)=(−5,−12)
The distance between P(0,0) and S(−5,−12) is:
d=(−5−0)2+(−12−0)2
d=25+144
d=169
d=13
Therefore, the distance between points P and S is 13 km.